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## Finance and capital markets

# Renting vs. buying (detailed analysis)

We explore a more detailed model, including a downloadable spreadsheet, that factors many of the considerations needed when deciding whether to rent a home vs. buying a home. Click here to download the Home Purchase Model spreadsheet.. Created by Sal Khan.

## Want to join the conversation?

- Mr. Khan - this is a great series, but there is one aspect I can't wrap my head around. What about after the mortgage is paid off, and all I'm paying is the property tax vs continuing to pay rent for X number of years. Please do a scenario of more than 10 years, how about one for 40 or 50 years? Thanks for a great website.(74 votes)
- Also, assuming you were wisely (even conservatively) investing that 450k over 30 years you are sure to have at least 1 mill at the end of 30 years. Assuming a yearly average of 8% net return you would have over 1.8 million :) houses don't appreciate that fast under normal circumstances.(32 votes)

- It sounds to me that best thing to do is to save enough money to outright purchase the house and not get a loan to pay the bank the interest on the loan. Then its a win win situation where you could rent the house out and have positive cash flow.(14 votes)
- That could work for some people. Just remember that while you save the money, you will still be paying rent.

Scenario #1: Pay rent for a long time while you save money to outright purchase a house.

Scenario #2: Pay rent for a shorter period of time then get a mortgage to buy your house.

Scenario #1 has higher rent expense, scenario #2 has higher interest expense. Neither of which is a win win and the cheaper option will depend on your situation.(20 votes)

- Remember take advatage of the standard deduction, which for 2011 will be: $11,600 for married taxpayers filing jointly. So at a tax rate of 30%, renters would have an additional $3,480 in tax savings that mortgage payers wouldn't recieve.(9 votes)
- Yes, I have the same concern. If you do not have enough deductions to benefit from
**itemizing your taxes**, then you would just stick with the**standard deduction**in both the renting and the buying scenarios. This would mean that, for you, there is no extra tax benefit in the buying scenario vs. the renting scenario. Only if you already benefit from itemizing or if your home is expensive enough to justify itemizing is there a tax benefit to owning a home. And even if owning an expensive home is enough to justify itemizing, it still isn't a fair comparison because the standard deduction is not represented in the renting model.

Set income tax to 0% if standard deduction is higher than itemized.(2 votes)

- Also, the "buyrent.xls" is not on the download page. Can you please post and remove this in the video comments?(5 votes)
- Real Estate is a speculation with good odds. You buy with debt when interest rates are low. You buy for cash when interest rates are high. When the million dollar house is up for rent, it does not rent for $3K, it rents at a price commensurate with market sale value considering a cap rate. 3% cap rate at the time of purchase is what you expect to rent it for. Remember rental houses are owned by somebody. Also, 4% interest from a bank when you borrow at 6%? No. There is usually a 4% spread from what you earn and what you pay. Also, when you rent you pay one or two months security deposit plus last months rent which on a million dollar house would be $4,200 per month about. If you paid $600K 7 years earlier for the $1 million dollar house today then you could rent it for less, but you would not likely do that as the market would be higher. hence your margins will be higher. Also, I do not think a person should ever consider property appreciation as that would go to the hedge against inflation category. One still has to buy at the right time and not at the high peaks, however over time even the high peak purchasers will do well but not in the short run as rental prices will soften and create unmanageable competition for your property. Peaks exist today in some markets, however there are other markets that are at low valleys in terms of costs. My formula for buying a property is: conservative rental value x 12 x 10 = How much I will pay. This looks for a 10% cap Gross. Less maintenance and HOA or community dues and capitol improvement expenses which have tax benefits, one is left with a 5% net cap rate. Of course it is not easy to get this model to be realized, however what is easy? Our property values rise in excess of the rate of inflation because people make poor purchase decisions and help to improve comps and make prices rise. Pay what the property is worth, not what the seller is asking. If the seller wants $700K but it's worth $550K then thats the offer. Do that 20 times and you will get a house at the right price. The million dollar house in your example that can only rent for $3K per month is worth about $500K(10 votes)
- Nice spreadsheet. However, if I extend calculations for all 30 years, I am not getting debt = 0 (row 28) at the end of month 360. Is that correct?

For 1,000,000 purchase price with 20% downpayment and 5% interest for 30 years, I got mortgage payments = 4,271.64. With this monthly payments, I still have $19,085 in debt at the end of 30 years.

On-line mortgage calculator gives me 4,294.57 mortgage payments and that does reduce debt to 0.

It seems there is an error in the spreadsheet. Is it?(5 votes)- Alessandro P., you are right - the issue is in the mortgage payment and your formula is correct.

More simpler Excel formula will be

=(B4-B5)**B6/12**(1+B6/12)^(B7*12)/((1+B6/12)^(B7*12)-1)

or even

=(B4-B5)*B6/12/(1-(1+B6/12)^(-B7*12))

or using Excel capabilities:

=-PMT(B6/12;B7*12;B4-B5)

Thanks to jtponsi and leball99 for pointing to EMI formulas(8 votes)

- The video is show max resolution is 240p, I cannot see the texts, is this only for me?(6 votes)
- So when you're done calculating, you determine which option is better by subtracting the equity of buying or renting (how much you saved vs how much you sold your home) by the liability or cash outflow of renting or buying to get the asset value. Whichever one results in a higher asset value is the better choice? Am I on the right track?(5 votes)
- This is my first comment, and this is because I just can not understand what the very last number on line 58 really means. So on our excel spreadsheet, it is 21,426.. and so does this number tell me that it is in fact better to buy? I don't understand since the conclusion of the previous 2 videos all point to the overwhelmingly consensus that renting is better than buying. Maybe I am confused about the present value benefit..(2 votes)
- Is it in brackets or without brackets? ...if it is within brackets that means a negative value and means you're better off renting.

If you get lost you can just compare the numbers on lines 54 and 56 - whichever is larger is a better fit for you (given your assumptions).

To be fair - I don't think this series of videos was trying to convince people to rent instead of buy...just to have you think the decision through for your own circumstances.(5 votes)

- Why doesn't he calculate Present value benefit of owning vs. renting for the amortization period of 30 years, instead of 10 years?(2 votes)
- As Sal say (12.00), normally, the average mortgage loan has 10 years expected life.

:)) Hey, are u Vietnamese?(3 votes)

## Video transcript

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.