Ayende @ Rahien

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The cost of money

This is just some rambling about the way the economy works, it has nothing to do with tech or programming. I just had to sit down recently and do the math, and I am pretty annoyed by it.

The best description of how the economy works that I ever heard was in a Terry Prachett’s book, it is called Captain Vimes’ Boots’ Theory of Money. Stated simply, it goes like this.

A good pair of boots costs 50$, and they last for 10 years and keep your feet warm. A bad pair of boots costs 10$ and last only a year or two. After 10 years, the poor boots cost twice as much as the good boots, and your feet are still cold!

The sad part about that is that this theory is quite true. Let me outline two real world examples (from Israel, numbers are in Shekels).

Buying a car is expensive, so a lot of people opts for a leasing option. Here are the numbers associated with this (real world numbers):

  Buying car outright Leasing
Upfront payment 120,000

42,094.31

Monthly payment (36 payments) 0

1,435.32

Buying the car (after 3 yrs) [optional] 0

52,039.67

The nice part of going with a leasing contract is that you need so much less upfront money, and the payments are pretty low. The problem starts when you try to compare costs on more than just how much money you are paying out of pocket. We only have to spent a third.

Let us see what is going to happen in three years time, when we wan to switch to a new car.

  Buying car outright Leasing
Upfront payment 120,000.00

42,094.31

Total payments 0.00

51,671.52

Selling the car -80,000.00

0.00

Total cost 40,000.00 93,765.83

With the upfront payment, we can actually sell the car to recoup some of our initial investment. With the leasing option, at the end of the three years, you are out 93,765.83 and have nothing to show for it.

Total cost of ownership for the leasing option is over twice as much as the upfront payment option.

Buying an apartment is usually one of the biggest expenses that most people do in their life. The cost of an apartment/house in Israel is typically over a decade of a person’ salary. Israel’s real estate is in a funky state at the moment, being one of the only places in the world where the prices keep going up. Here are some real numbers:

  • Avg. salary in Israel: 8,611
  • Avg. price of an apartment (in central Israel): 1,071,900

It isn’t surprising that most people requires a mortgage to buy a place to live.

Let us say that we are talking about a 1,000,000 price, just to make the math simpler, and that we have 400,000 available for the down payment. Let us further say that we got a good interest rate of the 600,000 mortgage of 2% (if you take more than 60% of the money you are penalized with higher interest rate in Israel).

Assuming fixed interest rate and no inflation, you will need to pay 3,035 for 20 years. But a 2% interest rate looks pretty good, right? It sounds pretty low.

Except over 20 years, you’ll actually pay: 728,400 back on your 600,000 loan, which means that the bank get 128,400 more than it gave you.

The bank gets back 21.4% more money. With a more realistic 3% interest rate, you’ll pay back 33% more over the lifetime of the loan. And that is ignoring inflation. Assume (pretty low) 2% per year, you would pay 49% more to the bank in 2% interest rate and 65% more in 3% interest rate.

Just for the fun factor, let us say that you rent, instead. And assume further that you rent for the same price of the monthly mortgage payment. We get:

 

Mortgage

Rent
Upfront payment 400,000.00 0.00
Monthly payment 3,000.00 3,000.00
Total payments (20 years) 720,000.00 720,000.00
Total money out 1,120,000.00 720,000.00
House value 1,000,000.00 0.00
Total cost 120,000.00 720,000.00

After 20 years, renting cost 720,000. Buying a house costs 120,000.  And yes, I am ignoring a lot of factors here, that is intentional. This isn’t a buy vs. rent column, it is a cost of money post.

But after spending all this time doing the numbers, it all comes back to Vimes’ Boots theory of money.

Comments

grega_g
06/23/2010 10:22 AM by
grega_g

Missing the end of post?

Andreas
06/23/2010 10:35 AM by
Andreas

The buy vs. lease car example is a bit flawed since you can buy the leased car for 52,039 and then sell it for 80000 and make 27961 back.

You could also argue that 52039 is a more accurate selling price then 80000.

Leasing is still the more expensive regardless.

Ayende Rahien
06/23/2010 10:39 AM by
Ayende Rahien

Andreas,

You are correct, but remember that with that route, you get reduced price because you would be selling the car as 2nd owner, not 1st owner.

Paul Stovell
06/23/2010 10:56 AM by
Paul Stovell

Are you missing a 0 here:

Avg. salary in Israel: 8,611

Ayende Rahien
06/23/2010 11:23 AM by
Ayende Rahien

Paul,

No, I don't.

In Israel we think about salaries per month vs. salaries per year.

Zach
06/23/2010 12:28 PM by
Zach

I believe you might have done the numbers Backwards for inflation adjustment. Because you are making (I'm assuming) a fixed payment size over the course of the 20 years, the Purchasing Power of each payment you are making is slightly less due to inflation. This means that the inflation adjusted cost of the home actually goes down in this scenario rather than up as you have shown.

A 2% mortgage with 2% inflation means the bank would actually Lose money in end. They amortized their 2% interest on the current value of the loan but you are paying them in future dollars.

I know you are simplifying, but another key difference you left out is that the home price should at minimum follow inflation over the long haul (ignoring any bubbles). So that 1,000,000 shekel house @ 2% inflation in 20 years is actually worth 1,000,000 * (1 + 0.02) ^ 20 = 1,485,947.40.

With buying though, there is an opportunity cost associated with the down payment, so let's assume you Just get inflation levels of returns on your investments over 20 years. That 400,000 shekel down payment has a future value in 20 years @ 2% of 400,000 * (1 + 0.02)^20 = 594,378.96.

So, if you rent, you've paid 720,000 shekels over the course of 20 years but that 400,000 is now worth 594,378 so the total cost to you is 720,000 - 594,378 = 125,621.04

If you buy, you paid the 400,000 shekels up front and then 720,000 shekels over the course of 20 years giving a total cost 1,120,000 shekels. But since the house is now worth 1,485,947.40. when you sell it you come out 365,947 shekels ahead.

The total investment benefit of buying in this situation over renting is 365,947 cash in hand after sale - -125,621 cash in hand after renting which is 491,568 shekels.

Basically, here is how buying normally will profit you. The bank amortizes the loan including interest in present value. However, your home's value increases as percentage of the base value of the home, which is a really large number, usually much larger than your down payment. Your down payment, if invested rather than used to buy a house, also increases as a percentage, but it has a much lower base value. As a result, the absolute growth of value on the house can be much higher than that of the down payment.

The tricky bit though, at least here in the US, is that the mortgage rates and the investment rates can be quite different (say 5% mortgage, 4% annual home price increase, 8% annual return from S&P Stock Index). So figuring out the true cost to own is quite complex. Furthermore, you add in things like maintenance and taxes and things get super muddy.

NC
06/23/2010 12:29 PM by
NC

So roughly 103k / yr in Israel, and you pay 1,000,000 for an apartment...

Average income in australia is something like 45k/r and in Sydney apartments are anywhere from 800k to 2 million... and prices are going up because of foreign investors cos this country is too fucking retarded to say NO.

Not only that interest rates are 5%+ with loans up to 100% of your mortgage.

Mike Curran
06/23/2010 12:34 PM by
Mike Curran

Man, with number twisting skills like that, you should be selling vacuum cleaners...

What are the odds that the boots will last ten years? What happens if they get damaged or stolen? What happens if "boots" go out of style and "knee boots" are in? What if you move to a place that you no longer need the boots?

In the house example, if you took that 400k and stuffed it in 5% bonds instead of a house you'd have 1,000,000 in cash at the end and you wouldn't be paying for home owner insurance and you wouldn't have to pay realtor fees to free up the money. If you risk it in the stock market and make 8% you'd have almost 2 million.

Numbers are great, they can show anything you like, if you don't have to based them on hard evidence.

Ayende Rahien
06/23/2010 12:36 PM by
Ayende Rahien

Zach,

No, I did not. At least not the way that it works in Israel.

Payments for the loan are typically tied to inflation, so as the inflation rises, so does the loan amount and the monthly payment.

The rest of the math works, sure.

If you invest the 400,000 in gov. bonds for 20 years (rate is currently ~4%), it actually gets much better.

And you can get bonds that follow the inflation curve, so you are actually getting a bit more.

Maintenance & insurance are big ticket items here, sure. Because as an owner you pay that, while as a renter you typically don't.

Taxes you pay whatever as renter or owner.

But I am not trying to argue rent vs. own, I am arguing more about people falling into the trap of "2% interest rate is cheap" ending up giving the bank back 30% as much money as they took, and that is discounting inflation

Ayende Rahien
06/23/2010 12:39 PM by
Ayende Rahien

Mike,

I am going to ignore the boots comments, because you seems to have missed the point.

For the house example, real estate tends to appreciate in value over time.

My aunt bought an apartment 20 years ago for 70,000$ which is now worth ~500,000$

But take a look at the car example, what is your counter point there?

Ayende Rahien
06/23/2010 12:42 PM by
Ayende Rahien

NC,

I gave an example of an average apartment, in Tel Aviv, you would be paying 2 mil easily for most good places.

prices are going up because of foreign investors cos this country is too fucking retarded to say NO.

I can agree with that statement as well, for the same reason.

Regarding interest rates, I intentionally gave very low interest rates, because I wanted to make the point there.

My parents once had a mortgage at 13%(!), scary.

Zach
06/23/2010 01:11 PM by
Zach

Ahh, I was wondering if it worked different there (which is why I explicitly called out the assumption of fixed payments).

Here in the US, for a "traditional" govt backed loan, the interest rate is Fixed. Since the purchase price of the home is also fixed at the beginning, you get a fixed amortization schedule where you pay the same each month, but more goes to principle and less to interest with each payment. Essentially you are paying like 90% interest and 10% principal for the first payment, but by the last payment you are paying nearly 100% principal.

If in Israel the interest you pay is something like "inflation + bank rate%" e.g. (2% inflation + 2% loan interest) then it definitely doesn't save you money like I was suggesting. However, hopefully over the long term, the wages track with inflation. If rent prices track 1:1 against typical mortgage payments like in the example above, then you will still come out ahead with the purchasing for one reason: The future value of the down payment if invested is a percentage of a much smaller base amount than the house. So as long as the bank rate keeps the Amount owed fixed (they don't track the present value of the home when determining your monthly payment) you will still come out ahead every time with these interest numbers.

What can make that mortgage interest rate NOT cheap, is when either:

The mortgage interest rate is significantly higher than the annual home value increase percentage

Or

If the investment return percentages are significantly higher than the delta of the annual home value increase and mortgage interest rate.

Basically when:

(Annual increase on large home value base price - Costs due to mortgage interest) > (Annual investment increase on smaller down payment)

Where monthly rent == monthly mortgage

If all you are trying to show is that 2% on a mortgage isn't "cheap" because you pay 21% in interest, you also need to counter with "keeping that 400,000 shekel down payment at rest also isn't cheap, because @ 2% inflation for 20 years that down payment is only worth 267,043 in inflation adjusted shekels"

Andrew Borodin
06/23/2010 01:13 PM by
Andrew Borodin

Hello.

I'm from Russia. Two years ago I bought car by a loan with 13% interest rate. And, it was good investment (: . Today my car costs more than it's initial cost, bank interest for 2 years and all these keeping expenses and oil. If I substract that driving increased my work time, I can include insurance in (list1). It seems to me like I'm trickster. (:

I like school problem on geometrical progression. Suppose we have a paper, which gives us right to recive 10 money units per year forever. Inflation rate is 10%/yr. How much does this paper cost?

It costs 110 today money units.

Ayende Rahien
06/23/2010 02:01 PM by
Ayende Rahien

Zach,

Here you typcially have fixed rate loans, variable rate loans (based on the central bank's interest rate) and fixed rate no inflation loans.

By default, as you probably guessed, all loans are inflation adjusted.

The amortization schedule is the same, btw. The catch here that every time that inflation index changes, so does the principal of the loan (and the payment).

Let us say that I took a 500,000 for 20 years. That would be 3,500 monthly, more or less.

Every month the gov. publishes the inflation index.

So on the second month, inflation is 0.5%, so another 2,500 is added to the principal of the loan, and the payment is adjusted accordingly.

And so on & so forth.

And the 21% return for 2% interest is without inflation

Ayende Rahien
06/23/2010 02:02 PM by
Ayende Rahien

Andrew,

That is quite interesting. Cars generally don't appreciate in value, what was the cause of that

Zach
06/23/2010 02:31 PM by
Zach

Oh wow, that's nuts. They actually adjust the principal of the loan for inflation and then take their interest rate against that new principal amount.

"And the 21% return for 2% interest is without inflation"

Ahh right, so if I understand correctly, in Israel with the way the loans typically track inflation, with all other things being fixed, unless home prices increase annually on average at a rate greater than (inflation rate + bank rate), you will pay more for the home over the course of the loan than it will be worth the day the loan is paid in full. This represents a A Positive Cost to your money. However, since rent rates track directly with mortgage rates AND since you keep "paying for the good over and over" because you build no equity, the Cost of the money is a much larger Positive for renting, similar to buying the cheap boots.

Is that what you are going for?

Andrew Borodin
06/23/2010 02:35 PM by
Andrew Borodin

At the begining of 2008 oil price was around $150, few monthes later it failed to $30. Russian economics is strongly correlated with this indicator, oil and gas is about 20% or more of GDP. So, rate Russian ruble to USD decreased by 30%. This 30%, in general, was forced by trader mobs. Car was imported, so it's price is in usd, while loan is in RuR. In 2009 import tax rate was increased to support internal car production. So, car's price rised again. Average sallary rises here faster then 13% a year, so demand on cars increased, it's price is rising.

I was not thinking about all these things when I was buying my car.

Dennis
06/23/2010 02:41 PM by
Dennis

Current mortage rate here in vietnam is around 16.7% pa :P

José F. Romaniello
06/23/2010 02:58 PM by
José F. Romaniello

I can't even think the same maths in Argentina where the anual rate for a loan is about 45%. (you heard right 45%)

Ayende Rahien
06/23/2010 02:59 PM by
Ayende Rahien

Zach,

That is pretty much it, yes.

Andrew Borodin
06/23/2010 04:33 PM by
Andrew Borodin

José,

Math is free, coherent and transcendental. You can do math anywhere.

Jason Young
06/23/2010 08:36 PM by
Jason Young

I am so proud to live with my parents and drive a 1996 Geo Metro with broken AC for this very reason.

Mikhail
06/23/2010 09:14 PM by
Mikhail

Speaking from purely mathematical point of view most (to be precise ~30%) of numbers in a exponential process start with 1. Is is called Benford's Law http://en.wikipedia.org/wiki/Benford's_law

Steve Py
06/23/2010 11:04 PM by
Steve Py

I had this same revelation when I considered leasing a Mazda many moons ago. The salesperson almost had me hooked... It looked like I could lease a car for less than the finance payments, and buy the car out at the end for pretty much the remainder of the purchase price, until I reviewed it again and noticed that this included the trade in of my existing car. Leasing cars is a ridiculously expensive option unless you own a business (or have a salary sacrifice option) so that you can claim payments & expenses pre-tax, or are vain enough to justify owning a new car every 2 years.

As for property: Australia is also in a bit of a bubble where property prices keep going up, and interest rates are on the climb again. There are a lot of ways to get trapped, but also a few options to save a lot of cash. The key difference between renting and buying is that rent is considerably lower than finance payments so the premise is that you can invest that extra money that isn't sunk into the house (and where up to 80% is fed to the bank as interest) into something that earns. Though most people just burn that extra cash on booze, vacations, or depreciating assets such as new cars and LCD TVs.

Sam
06/24/2010 02:58 AM by
Sam

Oren - you haven't done any NPV adjustments; the cost of money in the future is less than the cost of money now. In your rent example, if you'd invested the 400,000 shekels in <shares,> that earnt you, say 5% compounded annually, you'd end up with over 1,000,000 shekels after 20 years. Or, to put it another way, putting your 400,000 into an apartment for 20 years has an opportunity cost of 600,000 (depending on things like inflation & average rates of return), making you no better off over renting.

I'm not a financial expert, so I may not have explained that very well, but it's not quite as simple as adding up what you've spent over the life of the investment.

dotjoe
06/24/2010 02:09 PM by
dotjoe

Bottom line: Selling money is the most profitable business in the world.

Nick
06/24/2010 03:36 PM by
Nick

Just curious but what is the status of Better Place's implementation of the

battery switching stations in Israel? They have gotten a lot of good press from the Tokyo implementation but I haven't heard any progress on how or if it is still going in Israel.

Simeon Pilgrim
06/24/2010 07:40 PM by
Simeon Pilgrim

Hi Ayende,

Completely agree with the lease being the worse way to buy a car. Also you should really never buy a new car unless you can afford to buy it out right with cash, and not effect your cashflow. (due to deprecation)

The major point of a house is that if you rent for life, when you stop working you still have to pay for the rent, verse owning the house outright means you need less cashflow once you stop working, or you just can't afford to stop working.

Major point, don't be a slave to debt.

Uriel Katz
06/24/2010 08:14 PM by
Uriel Katz

Oren,

The funny part in israel is even a programmer(one of the most profitable career here in israel) is making 15000NIS on avg. can`t buy a home at centeral israel without a mortgage.

also the part about having 400K in the side is a very rare for a young person/couple(<30).

Steve Py
06/25/2010 12:12 AM by
Steve Py

I miss the financing deals in Canada/U.S. a while back before the major manufacturers were in so much trouble. I bought my Pontiac at 0.6% financing, and for a while GM and such were even offering 0% financing options. With my down payment and summing up the payments, financing my car at the time cost $600 over the purchase price. Not like my Honda here in Oz. I paid nearly 1/2 down, and paid off the last $8000 outright and the interest charges still added just shy of $2000 to the price of the car. :( Considering the dang things are about an extra 1/3rd more expensive than in Canada...

Raj Aryal
06/25/2010 09:03 PM by
Raj Aryal

Cheap is expensive. Think three times before you pay.

Rytis
06/26/2010 03:25 AM by
Rytis

You missed some points - what is better:

  • to take loan and to drive car NOW

  • wait 3 years, get all money and only then buy the car

Interest - is something like renting, you pay interest for renting a car 3 years, after that you buy car for normal price

Emmanuel Bernard
07/10/2010 07:03 AM by
Emmanuel Bernard

To add to Zach's argumentation, assuming you can pay the house cash, it's still better to get a loan and invest the money not locked in even if the interest rate is lower than the loan rate.

The key is that interest rates are compounds contrary to loans

katrina
07/23/2010 06:39 AM by
katrina

how much are the car loan and home loan interest rates of bank in israel today?

Ayende Rahien
07/23/2010 06:42 AM by
Ayende Rahien

Katrina,

I would say that it is 1% - 3%, probably

Comments have been closed on this topic.