Learn about Renting vs. Buying - detailed analysis Video

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Learn about Renting vs. Buying - detailed analysis

Welcome, so I've done this series of presentation about housing at least my thesis in why housing prices might have gone up and how you should maybe on simple terms think about the rent versus buy decision. But one thing has happened, a lot of people have said, oh so you're making over simplifying assumptions. You're assuming interest only a loan. You're not factoring in the tax deduction of mortgages of interest in your mortgage, which I did. But I did make some simplifying assumptions that we could kind of do back of the envelop math and just think about the main drivers are when you think about renting versus buying. But it is fair. You know, that’s just kind of the first cut you really should do a multiline model. Trying to figure out what could happen to you and then tweak your assumptions. Really figure out what's going to happen to you if housing appreciates-depreciates interest change. If you put 10 percent down or 20 percent down or whatever. So with that in mind, I've constructed this model what I call, this is the home purchase model. And you could 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 will be able to access it and maybe you want to follow along while you're watching this video. So just K-H-A-N- academy.org. I don’t know if you can read this on you tube. Downloads, D-O-W-N-L-O-A-D-S/buyrent.xls. So once you download it, let me explain what I assumed in the model. So the yellow, what I did in yellow, what this bright yellow and this less bright yellow is these are assumptions. These are the things that will drive the model and tell us whether over. And I calculated over 10 years. Over 10 years, whether we would do better renting versus buying. And if you download this model and when you 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 is driven by these inputs. So of course what matters in a home? Well the purchase price matters, right. So you just input it there. The down payment matters, you could if want, you can just write 20 percent of whatever the purchase price is. So you can write your exact number or you can just leave it the way I did and whatever the down payment percentage is. It will calculate it. This is the interest rate you assumed. 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 the interest, how long is the entire principal amount going to be paid often. So essentially a 30 year fix rate loan has a 30 year principal amortization. If you have a 10 year loan, you would put 10 year. This is the property tax rate. This is what I assumed, because I live in California. And most areas of California, that’s the property tax. This is what I assumed about annual maintenance. That’s just an assumption. Some houses might be less, it might be more. That’s for 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 0 if you don’t. This is annual insurance for things like hazard insurance and flood insurance or earthquake insurance or whatever insurance you need where you live. And then this bright yellow, I say, what is the assumed annual appreciation of the house itself. And this is a huge assumption, that’s why I put it into this bold yellow color. Because we’ll see later in this video that the some degree, to some degree, that assumption is one of the biggest drivers of assumptions. You can say that the model is very, very, very sensitive to that assumption. Here 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 the property tax. So if you can deduct $100 in interest and property tax if your marginal tax rate is 30 percent. So that means, you know, at what rate are you being taxed on every incremental dollar? If its 30 percent, that means a $100 deduction will save you $30. If your marginal tax rate is 28 percent, a $100 deduction will save you $28. So that’s where that comes in to play. The 2 percent, 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 assumed about. Well what is the general rate of inflation in our model that’s actually going to drive how this grow over the life of your loan. And then once you typed in all of these things, the monthly mortgage payment is calculated. I assumed that the interest compounds once a month, 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 you 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 in your return increases or the other way around, you would return with decrease. But anyway don’t want it to be too complicated. And then this is the 6 percent, I just assumed its 6 percent. You could 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, I don’t know, maybe I'm a good investor I could put it in the stock market. Maybe I can get 20 percent a year. Or maybe I'm really riskaverse and I put it in government bonds and I get 4 percent 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 percent, and I think I can get 10 percent of the stock market. I should actually put a 7 percent here. So we want to make sure that were 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. So let me just squeeze this a little bit. Doing this on YouTube, Excel on YouTube is a new thing for me. That’s not what I wanted to do. So let me unfreeze window. Okay. So now I can show you the rest of the model. So all of the assumptions that we did, that drives this model. Let me freeze the window right here. Window freeze, okay, that should make things a little bit easier. So this is the buying scenario, up to line 40. This says at period 0, what is the home value? And don’t type in anything here. It’s all automatically calculated. So period 0, what is your home value? And then it essentially uses depreciation numbers and each number is essentially a month. And I actually wrote that down here. And then it figures out what is the market value. But it’s completely driven by the depreciation number. This right here is the debt or essentially the principal payment on your mortgage or how much do you owe the bank. And as you see as months go by, when you pay the mortgage note, and I showed 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 at the interest on the amount you owe. And then obviously if you watched the video the 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, another way to do this, actually say, what am I worth or what is this investment worth to get that point? So these are kind of the important numbers in the home buying scenario. This driven by this interest on debt 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 essentially we 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 inflation rate, divide it by 12. And we multiply it by each of these months. The housing association dues, that once again is in a monthly basis. So we just took your assumptions divided by 12. Maintenance, same thing. Property tax, same thing, although I assume that your house gets reassess. So you're in a state where every year the assessor or every several years the assessor comes, 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 US. So actually, to some degree, the dollar value of property taxes is driven by this home value assumption up here. This income tax saving from interest deduction, this is assuming that that marginal tax rate. You can deduct the property tax and the interest on the debt. And then this is the total cash out flow, after adding back the income tax savings. So this is essentially how much cash goes out the door even after the tax saving every month in the buying scenario. That’s what that is. So hopefully that makes a little bit sense. So what we want to do is we want to figure out. Okay, 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 am going to use that cash to pay my rent and any other expenses associated with rent, really aren't much. To pay my rent and then put the rest in the bank. So what we are saying is, well, that assumption was you can rent a similar house for $2500, maybe right, maybe wrong. It’s up for you to play with. And of course it grows with inflation, obviously your rent doesn’t increase every month, but I assume it does really continuously. It’s a reasonable assumption I think. Although you can change it. You can only make it step up every year, excuse me. And then, this line down here tells us the savings while renting. Or how much, and I'm not saying this savings like something on sales like save money. But your savings in terms of how much you have in the bank. So if you rent it, instead of putting that $150,000 as a down payment, you could put it in the bank. So that would be your savings and count it period 0. And then your savings account in period 1 would be this amount of money and whatever you 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, I could show you. I could scroll through multiple periods. This model goes as far as Excel would let me. But the average house, if anyone whose traded mortgage bonds will tell you, the average house has an average mortgage loan of 10 year expected life. And that's on average, people tend to move or refinance. So what I do is I figure out, well, given your assumptions. Whatever, 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 calculate, what it tells is 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 percent to a broker, hopefully that won't be the case in 10 years and the internet will intermediate real estate brokers. But who knows. I apologize to you if you are a real estate 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. Discounted back to today. Actually, I'm at the present value, did I present value this numbers? No, I didn’t. So actually, this is 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 values. 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. Whenever you think, probably the inflation rate, and it would tell you today’s money. What is the benefit or the advantage of buying versus renting? Anyway, I've spent 14 minutes of your time. I encouraged you to download this model. Play with it. Then work out the assumptions, because I think that’s the important thing. You know, some people will make some sets of assumptions say, aha! I should rent. Others say, aha! I should buy. But they don’t realize that they made some assumptions that although it looks really reasonable. You know, like say I make this 3 percent annual appreciation assumption, right. That doesn’t seem crazy, but it’s amazing how much it will change the model if you make that 3 percent into a 1 percent. Or if you make it into a negative 1 or negative 2 percent. 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 study shows that real estate over the last 100 years is actually roughly grown, on real terms, maybe 1 or 2 percent. So actually 1 or 2 percent here isn’t that conservative. Actually, especially after big real estate boom, maybe prudent. So play with these assumptions and I think it will give you an intuition of what are the real drivers. And another big thing here, sometimes you don’t rent a similar home, you would rent a smaller home. So that would be different type of savings and there are tradeoffs there. But anyway, hopefully you’ll find this model useful. I think it should be. This is the biggest investments of their 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. Because this is about as serious as you can get. So enjoy. See you in the next video.

Khan Academy

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Welcome, so I've done this series of presentation about housing at least my thesis in why housing prices might have gone up and how you should maybe on simple terms think about the rent versus buy decision. But one thing has happened, a lot of people have said, oh so you're making over simplifying assumptions. You're assuming interest only a loan. You're not factoring in the tax deduction of mortgages of interest in your mortgage, which I did. But I did make some simplifying assumptions that we could kind of do back of the envelop math and just think about the main drivers are when you think about renting versus buying.
But it is fair. You know, that’s just kind of the first cut you really should do a multiline model. Trying to figure out what could happen to you and then tweak your assumptions. Really figure out what's going to happen to you if housing appreciates-depreciates interest change. If you put 10 percent down or 20 percent down or whatever. So with that in mind, I've constructed this model what I call, this is the home purchase model. And you could 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 will be able to access it and maybe you want to follow along while you're watching this video. So just K-H-A-N- academy.org. I don’t know if you can read this on you tube. Downloads, D-O-W-N-L-O-A-D-S/buyrent.xls.
So once you download it, let me explain what I assumed in the model. So the yellow, what I did in yellow, what this bright yellow and this less bright yellow is these are assumptions. These are the things that will drive the model and tell us whether over. And I calculated over 10 years. Over 10 years, whether we would do better renting versus buying. And if you download this model and when you 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 is driven by these inputs.
So of course what matters in a home? Well the purchase price matters, right. So you just input it there. The down payment matters, you could if want, you can just write 20 percent of whatever the purchase price is. So you can write your exact number or you can just leave it the way I did and whatever the down payment percentage is. It will calculate it. This is the interest rate you assumed. 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 the interest, how long is the entire principal amount going to be paid often.
So essentially a 30 year fix rate loan has a 30 year principal amortization. If you have a 10 year loan, you would put 10 year. This is the property tax rate. This is what I assumed, because I live in California. And most areas of California, that’s the property tax. This is what I assumed about annual maintenance. That’s just an assumption. Some houses might be less, it might be more. That’s for 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 0 if you don’t. This is annual insurance for things like hazard insurance and flood insurance or earthquake insurance or whatever insurance you need where you live. And then this bright yellow, I say, what is the assumed annual appreciation of the house itself. And this is a huge assumption, that’s why I put it into this bold yellow color. Because we’ll see later in this video that the some degree, to some degree, that assumption is one of the biggest drivers of assumptions. You can say that the model is very, very, very sensitive to that assumption. Here 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 the property tax. So if you can deduct $100 in interest and property tax if your marginal tax rate is 30 percent. So that means, you know, at what rate are you being taxed on every incremental dollar? If its 30 percent, that means a $100 deduction will save you $30. If your marginal tax rate is 28 percent, a $100 deduction will save you $28. So that’s where that comes in to play.
The 2 percent, 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 assumed about. Well what is the general rate of inflation in our model that’s actually going to drive how this grow over the life of your loan. And then once you typed in all of these things, the monthly mortgage payment is calculated. I assumed that the interest compounds once a month, 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 you 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 in your return increases or the other way around, you would return with decrease. But anyway don’t want it to be too complicated.
And then this is the 6 percent, I just assumed its 6 percent. You could 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, I don’t know, maybe I'm a good investor I could put it in the stock market. Maybe I can get 20 percent a year. Or maybe I'm really riskaverse and I put it in government bonds and I get 4 percent 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 percent, and I think I can get 10 percent of the stock market. I should actually put a 7 percent here. So we want to make sure that were 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. So let me just squeeze this a little bit. Doing this on YouTube, Excel on YouTube is a new thing for me. That’s not what I wanted to do. So let me unfreeze window. Okay.
So now I can show you the rest of the model. So all of the assumptions that we did, that drives this model. Let me freeze the window right here. Window freeze, okay, that should make things a little bit easier.
So this is the buying scenario, up to line 40. This says at period 0, what is the home value? And don’t type in anything here. It’s all automatically calculated. So period 0, what is your home value? And then it essentially uses depreciation numbers and each number is essentially a month. And I actually wrote that down here. And then it figures out what is the market value. But it’s completely driven by the depreciation number.
This right here is the debt or essentially the principal payment on your mortgage or how much do you owe the bank. And as you see as months go by, when you pay the mortgage note, and I showed 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 at the interest on the amount you owe. And then obviously if you watched the video the 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, another way to do this, actually say, what am I worth or what is this investment worth to get that point?
So these are kind of the important numbers in the home buying scenario. This driven by this interest on debt 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 essentially we 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 inflation rate, divide it by 12. And we multiply it by each of these months. The housing association dues, that once again is in a monthly basis. So we just took your assumptions divided by 12. Maintenance, same thing.
Property tax, same thing, although I assume that your house gets reassess. So you're in a state where every year the assessor or every several years the assessor comes, 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 US. So actually, to some degree, the dollar value of property taxes is driven by this home value assumption up here.
This income tax saving from interest deduction, this is assuming that that marginal tax rate. You can deduct the property tax and the interest on the debt. And then this is the total cash out flow, after adding back the income tax savings. So this is essentially how much cash goes out the door even after the tax saving every month in the buying scenario. That’s what that is.
So hopefully that makes a little bit sense. So what we want to do is we want to figure out. Okay, 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 am going to use that cash to pay my rent and any other expenses associated with rent, really aren't much. To pay my rent and then put the rest in the bank.
So what we are saying is, well, that assumption was you can rent a similar house for $2500, maybe right, maybe wrong. It’s up for you to play with. And of course it grows with inflation, obviously your rent doesn’t increase every month, but I assume it does really continuously. It’s a reasonable assumption I think. Although you can change it. You can only make it step up every year, excuse me. And then, this line down here tells us the savings while renting. Or how much, and I'm not saying this savings like something on sales like save money. But your savings in terms of how much you have in the bank.
So if you rent it, instead of putting that $150,000 as a down payment, you could put it in the bank. So that would be your savings and count it period 0. And then your savings account in period 1 would be this amount of money and whatever you 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, I could show you. I could scroll through multiple periods. This model goes as far as Excel would let me. But the average house, if anyone whose traded mortgage bonds will tell you, the average house has an average mortgage loan of 10 year expected life. And that's on average, people tend to move or refinance.
So what I do is I figure out, well, given your assumptions. Whatever, 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 calculate, what it tells is 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 percent to a broker, hopefully that won't be the case in 10 years and the internet will intermediate real estate brokers. But who knows. I apologize to you if you are a real estate 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. Discounted back to today.
Actually, I'm at the present value, did I present value this numbers? No, I didn’t. So actually, this is 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 values. 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. Whenever you think, probably the inflation rate, and it would tell you today’s money. What is the benefit or the advantage of buying versus renting?
Anyway, I've spent 14 minutes of your time. I encouraged you to download this model. Play with it. Then work out the assumptions, because I think that’s the important thing. You know, some people will make some sets of assumptions say, aha! I should rent. Others say, aha! I should buy. But they don’t realize that they made some assumptions that although it looks really reasonable. You know, like say I make this 3 percent annual appreciation assumption, right. That doesn’t seem crazy, but it’s amazing how much it will change the model if you make that 3 percent into a 1 percent. Or if you make it into a negative 1 or negative 2 percent. 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 study shows that real estate over the last 100 years is actually roughly grown, on real terms, maybe 1 or 2 percent. So actually 1 or 2 percent here isn’t that conservative. Actually, especially after big real estate boom, maybe prudent.
So play with these assumptions and I think it will give you an intuition of what are the real drivers. And another big thing here, sometimes you don’t rent a similar home, you would rent a smaller home. So that would be different type of savings and there are tradeoffs there.
But anyway, hopefully you’ll find this model useful. I think it should be. This is the biggest investments of their 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. Because this is about as serious as you can get. So enjoy. See you in the next video.

Transcription by: Scribe4you Transcription Services