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So ive done this series of presentations about housing and at least. My thesis thesis on why housing prices might have gone up and how you should maybe in terms think about the rent versus buy decision. But one thing.

Thats happened. A lot of people. Said.

Oh sal. Youre making oversimplifying assumptions. Youre.

Assuming interest only loans youre 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 thats 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 whats 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. Ive 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 khanacademyorg downloads buyrentxls its 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 khanacademyorg downloads buyrentxls 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 its 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 itll 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 youd 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. Thats the property tax.

This is what i assume about annual maintenance. Thats just an assumption. Some houses might be less might be more thats 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 dont 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 thats why i put it into this bold yellow color. Because well 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.

Its 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.

Thats where that comes into play the. 2 . Thats general inflation and what this assumption drives is well theres 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.

Thats 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 thats 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 doesnt increase your return increases or the other way around your return decreases. But anyway dont 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 dont put the 150000. Down deposit on the home and i put it in i dont know maybe im a good investor. I could put in the stock market maybe i can get 20 a year or maybe.

Im 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 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 let me just squeeze this a little bit excel on youtube is a new thing for me thats 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 dont type in anything here.

Its 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 its 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. Its 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 thats going to be the mortgage payment minus your interest insurance payment.

Its 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 youre in a state. Where every year or every several years.

The assessor comes says oh your house is worth more now so im going to raise your taxes. Thats not the case in a lot of parts of. California but its the case in many parts of the us.

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.

Thats 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 150000.

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 im going to use that cash to pay my rent and any other expenses associated with renting which really arent much to pay my rent and then put the rest in the bank.

So what were saying is well that assumption was that you can rent a similar house for 2500. It may be right it may be wrong. Its up for you to play with and of course it grows with inflation slowly obviously your rent doesnt increase every month.

But i assume it does fairly continuously its 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 im not saying the savings from you know somethings 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 150000.

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 whos traded mortgage bonds will tell you the average mortgage loan has a 10 year expected life because thats 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 thats what the average american does after 10 years. And so what is the transaction cost you pay 6 to a broker. Hopefully that wont 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 lets 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 didnt so actually. This was meant to be the present value. Im 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 todays money. What is the benefit or the advantage of buying versus renting anyway.

Ive 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 thats the important thing. Some people theyll make some set of assumptions. And say.

Ah ha. I should rent or they say. Ah ha.

I should buy. But they dont realize that they made some assumptions that although it looks really reasonable. Lets say i make this 3 annual appreciation assumption that doesnt seem crazy.

But its amazing how much itll change the model if you make that 3 into a 1 or if you make it into even a negative 1 or negative 2. . Its completely possible its 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 isnt that conservative and actually especially after a big.

Real estate boom may be prudent. So play with these assumptions. And i think itll give you an intuition of what are the real drivers.

Another big thing sometimes you dont rent a similar home youd rent a smaller home. So that would be a different type of savings and there are trade offs there. But anyway hopefully youll 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 id 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.

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