So I've done this series of presentations about housing.

And at least, my thesis on why housing prices might have gone

up, and how you should maybe, in simple terms, think about

the rent-versus-buy decision.

But one thing that's happened, a lot of people said, oh, Sal,

you're making oversimplifying assumptions.

You're assuming interest-only loans.

You're not factoring in the tax deductions of mortgages,

et cetera, of interest on your mortgage.

Which I did, but I did make some simplifying assumptions.

So that we could kind of do back of the envelope math, and

just think about what the main drivers are when you think

about renting versus buying.

But it is fair.

That's just kind of a first cut.

You really should do a multi-line model, trying to

figure out what could happen to you.

And then tweak your assumptions.

And really figure out what's going to happen to you if

housing appreciates, depreciates.

If interest rates change.

If you put 10% down, or 20% down, or whatever.

So with that in mind, I've constructed this model.

What I called, this is the home purchase model.

And you can download it yourself and play with it.

I think this will prove to be useful for you.

You can download it at khanacademy.org/

downloads/buyrent.xls.

It's an Excel spreadsheet.

So if you have Excel, you should be able to access it.

And maybe you want to follow along while

you watch this video.

So just khanacademy.org/ downloads/buyrent.xls.

So once you download it, let me explain what I

assumed in the model.

So what I did in yellow, both this bright yellow and this

less bright yellow, these are our assumptions.

These are the things that are going to drive the model, and

tell us whether over -- and I calculated over 10 years --

whether we will do better renting versus buying.

And so if you download this model and want to play with it

yourself, unless you are fairly sophisticated with

Excel, the only things you should change are

the things in yellow.

Everything else is calculated.

And it's driven by these inputs.

So of course, what matters in a home?

Well the purchase price matters.

So you just in put it there.

The down payment matters.

You could, if you want, you can just write like I wrote,

20% of whatever the purchase price is.

So you can write the exact number, or you can just leave

it the way I did.

And whatever the down payment percentage is,

it'll calculate it.

This is the interest rate you assume.

This is the principal amortization.

So principal amortization just means, well, if I just keep

paying this mortgage, after how long is the entire

principal amount -- not just interest, how long is the

entire principal amount going to be paid off in?

So essentially, a 30-year fixed rate loan has a 30 year

principal amortization.

If you have a 10-year loan, you'd put 10 here.

This is the property tax rate.

This is what I assume because I live in California, and in

most areas of California, that's the property tax.

This is what I assume about annual maintenance.

That's just an assumption.

Some houses might be less, might be more.

That's up to you to decide.

This is housing association dues.

Maybe if you live in a community that has a shared

golf course, or a shared pool or something.

Put it at 0 if you don't.

This is annual insurance, for things like hazard insurance,

and flood insurance, earthquake insurance, or

whatever insurance you need where you live.

And in this bright yellow, I say, what is the assumed

annual appreciation of the house itself?

And this is a huge assumption.

And that's why I put it into this bold yellow color.

Because we'll see later in this video that to some

degree, that assumption is one of the biggest drivers of

assumption.

Or you could say the model is very, very, very sensitive to

that assumption.

Here, this is your assumed marginal income tax rate.

And why does that matter?

Well because you can deduct the interest that you spend on

your mortgage.

And also you can deduct, actually, the property tax.

So if you can deduct $100 in interest and property tax, if

your marginal tax rate is 30% -- so that means at what rate

are you being taxed on every incremental dollar.

If it's 30%, that means a $100 deduction will save you $30.

If your marginal tax rate is 20%, a $100 deduction will

save you $20.

So that's where that comes into play.

The 2%, that's general inflation.

And what this assumption drives is, well, there's going

to be some inflation on things like housing association dues,

annual maintenance, insurance.

And so this, what you assume about, well, what is just the

general rate of inflation, in our model that's actually

going to drive how these grow over the life of your loan.

And then once you type in all of these things, the monthly

mortgage payment is calculated.

I assumed that the interest compounds once a month.

You can, if you know your geometric series, you can go

in there and you can tweak it around so it compounds more

frequently or less frequently.

But my understanding is that most

mortgages compound monthly.

And then this right here, so this is everything that's

driving the buying a home decision.

Now these assumptions are so that we can make a comparison

to, well, what if instead of using that down payment to buy

a house, what if we actually just save that down payment,

put it in the bank, and rent a house instead.

So this is cost of renting a similar home.

This is the annual rental price inflation.

And I would argue, to some degree, that rental price

inflation over the long term should not be that different

than housing price inflation.

Because to some degree, rental is kind of the

earnings on a home.

And if earnings increase and the overall asset doesn't

increase, your return increases.

Or the other way around.

Your return decreases.

But anyway, don't want to get too complicated.

And then this is the 6%, or I just assume it's 6%.

You can change it.

This is what you assume that you can get on your cash.

So if I don't put the $150,000 down deposit on the home, and

I put it in, I don't know, maybe I'm a good investor.

I could put in the stock market.

Maybe I can get 20% a year.

Or maybe I'm really risk averse, and I put it in

government bonds, and I get 4% a year.

So this is the assumption that you get in on that.

And it actually should be an after-tax return on that cash.

So if my tax rate is 30% and I think I can get 10% percent on

the stock market, I should actually put a 7% here.

So we want to make sure that we're completely

accurate for taxes.

So now let me explain the rest of the model to you.

I want to make sure that I can fit it all within this window.

Let me just squeeze this a little bit.

Excel on YouTube is a new thing for me.

That's not what I wanted to do.

So let me unfreeze the window.

OK.

So now I can show you the rest of model.

So all those assumptions that we did,

that drives this model.

Let me freeze the window right here.

OK.

That should make things a little bit easier.

So this is the buying scenario, up to line 40.

This says, OK, at period zero, what is the home value?

And don't type in anything here.

It's all automatically calculated.

So at period zero, what is your home value?

And then it uses essentially the appreciation numbers.

And each period is essentially a month.

I actually wrote that down here.

And then it figures out, what is the market

value of your home?

And it's completely driven by that appreciation number.

This right here is the debt, or essentially the principal

payment on your mortgage, or how much do

you owe to the bank.

And as you see, as months go by, when you pay the mortgage

note -- and I show that right here, this mortgage payment.

Some amount of that, which is line 33, the principal paid.

Some of that goes to decrease the amount you owe.

And then a lot of it, especially initially, goes to

be actually the interest on the amount you owe.

And then obviously, if you watch the video on

introduction to balance sheets, your equity in the

home is the value of the home minus the debt, or minus what

you owe the bank.

So this actually calculates your equity.

Or essentially, one way to view it, is actually to say,

well, what am I worth?

Or what is this investment worth to me at that point?

So these are kind of the important numbers in the home

buying scenario.

It is driven by-- This interest on debt, it's

calculated by what interest rate you assume, times the

debt you owe and the period before.

The mortgage payment, we calculated that before, using

our mathematical knowledge of geometric series.

The paid principal, that's going to be the mortgage

payment minus your interest. Insurance payment, it's on a

monthly basis, right?

So we essentially took whatever our annual insurance

payment was and we divide it by 12.

But then we grow it by the rate of inflation

on a monthly basis.

So we took the inflation rate, divided by 12, and we

multiplied by each of these months.

The housing association dues, once again, this is on a

monthly basis.

So we just took your assumption, divided by 12.

Maintenance, same thing.

Property tax, same thing.

Although I assumed that your house gets reassessed.

So you're in a state where every year, or every several

years, the assessor comes, says, oh, your house is worth

more now, so I'm going to raise your taxes.

That's not the case in a lot of parts of California.

But it's the case in many parts of the U.S. So actually

to some degree, this, the dollar value, the property tax

is driven by this home value assumption up here.

This income tax saving from interest deduction, this is

assuming that at that marginal tax rate, you can deduct the

property tax and the interest on the debt.

And then this is the total cash outflow after adding back

the income tax savings.

So this is essentially how much cash goes out the door,

even after the tax savings, every month,

in the buying scenario.

That's what that is.

So hopefully that makes a little bit of sense.

So what we want to do is, we want to figure out, OK, you

could do that.

You could buy the house, put $150,000 down.

And every month put this much out, and as you see that

number grows.

The mortgage is the same, but a lot of these expenses grow

with inflation.

But I want to compare that to what happens if I take that

exact amount of cash, after adjusting for how much money I

get back from taxes.

And if I said, well, I'm going to use that cash to pay my

rent and any other expenses associated with renting--

which really aren't much-- to pay my rent, and then put the