Welcome. 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 rest in the bank. So what we're saying is, well,

that assumption was, that you can rent a similar

house for $2,500. It may be right, it

may be wrong. It's up for you to play with. And of course it grows with

inflation slowly.

Obviously your rent doesn't

increase every month, but I assume it does fairly

continuously. It's a reasonable assumption

I think. Although you can change it. You can make it only

step up every year. And then this line down

here tells us the savings while renting. And I'm not saying the savings

from, you know, something's on sale so I save money. But your savings in terms of how

much you have in the bank. So if you rented instead of

putting that $150,000 as a down payment, you could have

put it in the bank. So that would be your savings

account at period zero. And then your savings account

at period one would be this amount of money and whatever

return you got it, plus the difference between your

cash out from buying a home and your rent. So this is your savings. So what I do in this model —

and I could show you, I could scroll through multiple

periods.

Yeah, this model actually goes

as far as Excel would let me. But the average house — anyone

who's traded mortgage bonds will tell you– the

average mortgage loan has a 10 year expected life. Because that's when, on average,

people tend to move or refinance. So what I do is I figure out,

well, given your assumptions — you can make your own

assumptions — given your assumptions, what is

your home value? So let me make sure

I can get to that. So given your assumptions, what

this calculates is, well, it tells you what the home value

is after 10 years, your debt after 10 years, your home

equity after 10 years.

And it assumes you were

to sell your house. Because that's what the

average American does after 10 years. And so what is the

transaction cost? You pay 6% to a broker. Hopefully that won't be the

case in 10 years and the internet will dis-intermediate

real estate brokers, but who knows. I apologize to if

you are broker. And then this line, line 54,

that tells you what the net cash is if you sell your

house at a market price, you pay the broker. This number right here is much

simpler to some degree. It just tells you, well

let's say you decided not to buy the house. Given all your assumptions, how

much would you have saved in the bank at that time? And so this number right here,

this number is the difference between those two numbers

in 10 years, discounted back to today. Actually I meant to

present value it. But did I present value

these numbers? Oh no, I didn't. So actually this was meant

to be the present value. I'm going to correct that

before you actually play with the model.

Right now I just took the 10

year value, so this is the value in year 10. This is the difference

between the two. The present value would be if

you discount this by some discount rate. Whatever you think, probably

the inflation rate. And it would tell you in today's

money, what is the benefit or the advantage of

buying versus renting? Anyway I've spent 14 minutes

of your time. I encourage you to download this

model, play with it, and then work out the assumptions. Because I think that's

the important thing. Some people, they'll

make some set of assumptions and say, ah-ha! I should rent. Or they say, ah-ha! I should buy. But they don't realize that they

made some assumptions. That although it looks really

reasonable, let's say I make this 3% annual appreciation

assumption. That doesn't seem crazy. But it's amazing how much it'll

change the model if you make that 3% into a 1%, or if

you make it into even a negative 1% or negative 2%.

It's completely possible. It's happened before in the past

that you have flat real estate prices for a significant

period of time, even 10 years. And actually most of the studies

show that real estate, over the last 100 years, has

actually roughly grown, in real terms, maybe 1% or 2%. So actually 1% or 2% percent

here isn't that conservative. And actually especially after

a big real estate boom, may be prudent. So play with these

assumptions. And I think it'll give you

an intuition of what are the real drivers. Another big thing — sometimes

you don't rent a similar home. You'd rent a smaller home. So that would be a different

type of savings. And there are trade-offs

there. But anyway, hopefully you'll

find this model useful. I think it should be. People, this is the biggest

investment of their life.

They should do serious analysis

when they think about how they want approach it. And I'd like to think

that this is fairly serious analysis. This is about as serious

as you can get. So enjoy! See you in the next video..