I’ve done this series of presentations about housing and my thesis on why housing prices might have gone up, and how in simple terms you should think about the rent versus buy decision. But one thing that’s happened, a lot of people have said, Sal, you’re making oversimplified assumptions. You’re assuming interest-only loans. You’re not factoring in the tax deductions of interest on your mortgage. Which I did, but I did make some simplifying assumptions so we could do back of the envelope math and just think about what the main drivers are when you’re thinking about renting versus buying.

You really should do a multi-line model trying to figure out what could happen to you and then tweak your assumptions. Figure out what’s going to happen if housing appreciates, depreciates, if interest rates change, if you put 10% down, 20% down, or whatever. With this in mind, I’ve constructed this model, I call it 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 as you watch this video.

Once you download it, let me explain what I assumed in the model. The yellow, these are our assumptions. These are the things that are going to drive the model and tell us over 10 years whether we will do better renting versus buying.

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 what’s in yellow. Everything else is calculated and is driven by these inputs. So of course, what matters in a home? The purchase price matters. You could write the exact number or you could just leave it the way I did it. And whatever the down payment percentage is, just enter it.

Principal amortization just means, if I keep paying this mortgage, 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

This is housing association dues. Maybe if you live in a community that has a shared golf course, and a shared pool or something. Put it at $0 if you don’t. This is annual insurance for things like hazard insurance and flood or earthquake insurance or whatever you need where you live. And then this bright yellow, what is the assumed annual appreciation of the home 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. Or you could say that model is very sensitive to that assumption.

Here, this is your assumed marginal income tax rate. And why does that matter? Because you can deduct the interest you spend on your mortgage, and also you can deduct 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. 30%, that means $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 there’s going to be some inflation on things like housing association dues, insurance. So what you assume about this general rate of inflation, in our model, that’s 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 assume that the interest compounds once a month. If you know your geometric series, you can go in and tweak it around so that it compounds more or less frequently. But my understanding is that most mortgages compound monthly. So this is everything that’s driving the buying a home decision.

These assumptions are, what if, instead of using that down payment to buy a home, what if we actually just save that down payment, put it in the bank, and rent a home instead. This is cost of renting a similar home. This is annual rental price inflation over the long term should not be that different than home price inflation. Because to some degree, rental price inflation is kind of the earnings on a home. And if earnings increase, and the overall asset doesn’t increase, then your return increases. Or the other way around, your return would decrease.

This is the 6%, I just assume it’s 6%, but you can change it. This is what you assume you can get on your cash. So if I don’t get the $150K deposit on the home, and I put it in, maybe I’m a good investor. Maybe I could put it in the stock market, 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, and it should be an after tax return on that cash. So if my tax rate is 30%, and I think I can get 10% on the stock market, I should put 7% here. We want to make sure that we’re completely accurate for taxes.

Now let me explain the rest of the model to you. And I want to make sure that I can fit it all within this window. So now I can show you the rest of the model. All the assumptions that we did, that drives this model. So this is the buying scenario, up to line 40. So this says, at period zero, what is the home value? And don’t type anything in here. It’s all automatically calculated. So period zero, what is your home value? And then it uses essentially the appreciation numbers. And each period is a month.

It figures out what is the market value of your home. And it’s completely driven by the appreciation number. This right here is the debt, or essentially the principal payment on your mortgage, or what 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 the interest that you owe.

Obviously, if you watched 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. One way to view it is to say, what am I worth? What is this investment worth to me at that point. So these are the important numbers in the home buying scenario, and it’s driven by this interest on debt. It’s calculated by what interest rate you assume times the debt you owe in 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 your mortgage payment minus your interest. Insurance payment is on a monthly basis. So we took our annual insurance payment and divided by 12, but then we grow it by the rate of inflation on a monthly basis. So we took the inflation, divided by 12 and grew it by each of these months. The housing association dues. That’s once again on a monthly basis.

We just took your assumption, multiplied it by 12. Maintenance, property tax, same thing. Although I assume that your home gets reassessed. So you’re in a state where every year the assessor comes and says, your home is worth more now so I’m going to raise your taxes. That’s not the case in a lot of parts in California. But it’s the case in many parts of the US. So to some degree, this dollar value of the property tax is driven by this home value assumption 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 this is the total cash outflow. After adding back income tax savings. So this is essentially how much cash goes out the door every month even in the buying scenario. That’s what that is.

Hopefully that makes a little bit of sense. What we want to do is figure out, you could do that. You could buy a home, put $150K 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, I am going to use that cash to pay my rent, and any other expenses associating with renting, to pay my rent and then put the rest in the bank.

What we’re saying is, that assumption was that you could rent a similar home for $2500. May be right. May be wrong. It’s up for you to play with. And of course it grows with inflation, slowly. Obviously, your rent doesn’t grow every month, but I assume it does. It’s a reasonable assumption, I think. You could make it step up only every year.

This line down here tells us the savings while renting, and I’m not saying savings, like something’s on sale and you save money, but your savings. So how much you have in the bank. So if you rented, instead of putting that $150K as a down payment, you could have put it in the bank. So that would have been your savings account at period zero. So your savings at period one would be this amount of money at 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, it goes as far as Excel would let me.

The average home, as anyone who’s traded mortgage bonds will tell you, the average mortgage loan has as 10-year expected life. That’s when people tend to move or tend to refinance. So what I do is figure out, given your assumptions. Make your own assumptions. Given your assumptions, what is your home value. So let me make sure I can get to that.

Given your assumptions, this calculates the home value after ten years, your debt after ten years, your home equity after ten years, and then assumes you were to sell your home. Because that’s what the average American does after ten years. And so what is the transaction going to cost you? You pay 6% to a broker, hopefully that won’t be the cash in 10 years and the internet will do away with real estate brokers, but who knows? I apologize to you if you are a broker, and then this line tells you what the net cash if you sell your home at a market price, you pay the broker. This number right here is much simpler to some degree. It just tells you, let’s say you decided not to buy the home, given all your assumptions. How much would you have saved in the bank at that time?

This number right here, this number is the difference between those two numbers in 10 years, discounted back to today. And actually I meant to present value it. But did I present value these numbers? I didn’t. This was meant to be the present value. I’m going to correct that before you actually play with the model. 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 rate, probably the inflation rate, and it would tell you in today’s money what is the benefit or the advantage of buying or renting.

I’ve spent 14 minutes of your time. I encourage you to download this model. Play with it. And then work out the assumptions. Some people, they’ll make some set of assumptions and say, aha! I should rent. Or they’ll say aha! I should buy.

They don’t realize that they made some assumptions that although they look really reasonable, like let’s say I make this 3% annual appreciation assumption. That doesn’t seem crazy. But it’s amazing how much that’ll change the model, if you make that into a 1%. Or if you make it a -1, or -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 roughly grown on real terms maybe 1 or 2 %. So a 1 or 2% isn’t that conservative. And 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. And another big thing, sometimes you don’t rent a similar home. You rent a smaller home. So that would be a different type of savings. And there are trade offs there.

Anyway, hopefully you’ll find this model useful. This is the biggest investment of people’s lives. They should do serious analysis when they think about how they want to approach it. And I like to think this is fairly serious analysis. This is about as serious as you can get. So enjoy! See you in the next video.