# Renting vs. Buying (detailed analysis) | Housing | Finance & Capital Markets | Khan Academy

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
and play with it. I think this will prove
be able to access it. And maybe you want to
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

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

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,
assumptions — given your assumptions, what is
your home value? So let me make sure
I can get to that.

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

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..