Renting vs. buying (detailed analysis)

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.