Appreciation Rates

By playing around with the spreadsheet that we built, we will soon notice that a very important factor in the decision should be the appreciation rate. It is also the most difficult parameter to estimate. Think about it. You know the interest rate - just go ask the bank what you can get. You can easily find out the property tax rate - just make sure you put in the right one based on what district you're buying it in. Maintenance cost can be a little off, but you do have the ability to affect that by cutting down when you're spending too much. Rental increments is also a guess, but it usually tags inflation pretty well. And you can get much more reliable data on inflation rates than housing appreciation rates.

Let's say you will sell the house at the end of the loan. If you are married, you get the first $500,000 appreciation tax free, but the rest is taxable as long term capital gains. If we fix our other assumptions, and change the home appreciation rate, we will get the chart below. Interstingly enough, the breakeven point for buying a house is around 5%. In fact, I actually assumed a starting rent of $1800 a month, which is quite high in today's market. If you are willing to rent at a lower standard, the breakeven point will be even higher.

Rent vs Buy Analysis

We will now try our hand at the age-old question - whether to buy or to rent. First of all, keep in mind that this is a very basic analysis. Most importantly, it assumes that you only have two options - to rent for 30 years, or to buy a house and keep it for 30 years. A lot of calculators online make similar assumptions. This assumption makes the analysis much easier, but in the end, rather unrealistic. You don't have to do one or the other. You can rent this year, and buy the next. You can sell halfway through. It is possible that one of these other strategies could be better than the two we are considering now. But, this is a starting point.

The analysis is straightforward. From the previous post, we know the outgoing cash flow of buying a house, and the value of the house at the end of 30 years. We can also calculate the savings you make each year from renting, and the resulting amount you will get from investing it at a certain rate of return. Compare what you have at the end of 30 years, and you can immediately see which one is better.


Savings from renting is straightforward. First of all, you saved on the down payment. Every year after that, you save on the outgoing cash flow from buying a house minus your annual rent. Don't forget that you will earn interest on what you already have as well. Finally, interest income is taxable at 15% if it can be treated as long term capital gain.

Although the last line shows your worth in dollar amounts, it is important to note that the left one is the value of a house, and the right one is in investments that have already been taxed. If you are planning to sell this house at the end of the 30 years, you will have to subtract taxes from this amount. On the other hand, you can buy a house with your savings on the right. But in the latter case, you will be paying higher property tax on your new house.

Finally, do not read too much in the results from this particular example. This post is merely to illustrate the methodology. The results depend very heavily on the interest rates, appreciations rates, etc, and you should play around with these numbers to understand how things change when they change.

Cost of Buying a House

Now that we can calculate premiums, and understanding the inner workings of a loan, we can look at the bigger picture, and analyze the cash flow of buying a house. Granted, the loan and the down payment are a major factor in your overall cash flow, but there are others. The spreadsheet below illustrates how costs are incurred over time.

Property tax. That's right, if you have property, you have to pay taxes on it. Usually, the taxed amount is small compared to the value of your property, but because home values are in the hundreds of thousands of dollars, this tax can be a significant chunk of your cash flow out. There are usually two ways of calculating property tax. (1) Multiplying a flat amount by a fraction of your home's assessed value, or (2) Multiplying a percentage by the total assessed value of your home. They are both the same thing, just different calculations. For our purposes, we will take the price to be the assessed value, and property tax to be 1.25% of that. You should change that percent multiple depending on where you live. 1.25% is high for many places.

Maintenance Costs. A lot of people forget or underestimate how much it is to maintain a house. In our spreadsheet, maintenance is a catch-all for insurance, new furniture, fixing broken water heaters etc. We assume that it is a fixed percentage on the market value of the house ( not the original price ). Therefore, expect this number to grow. If you don't believe that it should grow with your house appreciation, it should at least grow with inflation. I assumed 1%, which is conventional wisdom.

Tax deductions. Property tax and interest are deductible, so you can subtract it from your gross income before calculating your other taxes. Good thing we know how to calculate how much we pay in interest, right? To get the exact amount on how much you can get back, you will need to actually do your taxes, and this amount will be different for everyone. As a rough estimate, I think 30% is pretty reasonable.

Total Cost. We can now easily calculate the total out of pocket costs that you will be paying for the next 30 years. Under our assumptions, these numbers will increase over time, because of the maintenance costs.

Loan Calculator: Beyond Toy Problems

If you understood everything that was going on in the toy problem, it will be quite easy to extend it to something more realistic. First, reserve a cell to contain the number of years, and change the 5 in your premium calculation to the value of that cell.

The next thing you have to do is to make the box below bigger, so that it covers 30 years. That's it! Now you have your own loan calculator. Just put in the amount of your loan, the interest at which you are borrowing at, and the number of years. The premium will be automatically calculated from the formula. On top of that, you can also see how much you pay in interest each year!

You can also add some extra pizzazz with a cell for the price of the house, and the down payment. Your loan will just be the first value minus the second.

Do Homeowners Really Get Richer?

There is an article on Yahoo Finance today by David Bach, who is rather optimistic about the current real estate market. I think he was trying to sell his book. I haven't read the book, and from his arguments in the article, I can't really recommend it, either.

The aim of this blog is to look at facts objectively. The author bases his claims on five arguments below, to which I will add some comments. We will hopefully get a chance to revisit these issues in a more in-depth manner in the future.

1) The first statement that he makes is that owning a house is cheaper than renting. Is that really true? I believe he is more correct when he says that there are "certain circumstances in certain markets" where renting is more beneficial in the short run. Well, rent is relatively low these days, and some would say the housing market is overheated, w0uld now qualify as a certain circumstance in a certain market?

As a resident of the Bay Area, I know that you can easily rent a small two bedroom house for $1500/month these days. Just check craigslist. But if you are looking for similar quality in a similar neighborhood, a condo might go for $350,000. For a house, be prepared to pay much more than that. Also, an assumption of 5% per year for annual rent increase is a little high, don't you think?

2) Leverage is a two-edged sword. Sure, things are great when they are going the right way. Leverage magnifies your gains. But if things start going the other way, you can also be in deep trouble. If you like leverage that much, foreign currency trading will actually allow you to win or lose that amount of money in a much shorter period of time. Though you shouldn't do it unless you know what you are doing.

3&4) It is true that homeowners have tax breaks, and renters usually don't. Though this is one factor into the entire equation, and you should take into account all the factors before you decide which option is better. By the way, he forgot to mention that homeowners have to pay property tax.

5) Are non-homeowners not savers too? If you are buying a house to live in, wouldn't your consumption go up? Think granite countertops, or that nice leather sofa. As a renter, I know that I rent at a lower standard than what I would buy at. I don't buy furniture that I would otherwise buy for my own house. Where does the extra money go? Into my bank account, into stocks, into bonds. If I keep this up, guess what? I'll be richer too! But the important thing is, which option saves more?

So, don't get excited about arguments that sound right. Instead of taking someone's statement at face values, ask to see the numbers, and learn how to analyze them.

A Better Way to Calculate Your Premiums

If you did the example in the previous post, you will soon find yourself grumbling to yourself, "There has gotta be a better way to get the premiums". That's right. Trial and error is great for illustrative purposes, but we can accomplish the same thing with a little bit of math.

In one of our earlier posts, we talked about evaluating cash flows by taking the present value. We will use that technique here to figure out our premiums. Let's call our annual premium $P. That is the amount that we will pay at the end of every year. Assuming that the interest rate is i, the present value of five annual payments would be:

That should be equal to the amount of the loan you took out. If we denote that as $L, we get the following equality.

A little bit of algebra will yield the following results.

Now instead of using the trial and error method, you can plug this formula into your Excel spreadsheet and watch the numbers work themselves out.

Loan Calculator: A Toy Problem

My advisor once said, "If you want to end up with something large that works, always start off with something small that works, instead of something large that doesn't work."

So let us start off small. Forget about 30 year loans with monthly payments. For this example, we are going to deal with 5 year loans with annual payments.

First, let us put down the amount of your loan and the prevailing interest rate. Put in a box for the premiums too, but leave it blank. You can change these numbers later on to see how your cash flows change with them.

Now let us put in a box for our cash flow calculations ( see fig. below ). In the first column, we have the amount still owed. The second column will keep track of the interest that is accumulated on the loan. The third column will track the premiums that you pay over the five years.

At the time you take out the loan, what you owe is what you took out, right? Right. This does not work like buying a new car, where the value drops 15% as soon as you drive it off the lot. So, in the "Now" box of the "Amount Owed" column, go ahead and make that equal to the cell containing the amount of your loan. As soon as you press Enter, that number will show up as the value in C2. If you change C2 later on, the numbers in this box will change with it.


Next thing to do is to see what the interest will be for the first year. Simply take the amount that you owe, and multiply that by your interest rate!

When we think about loans, most of the time, we are thinking about fixed payment loans. You pay the same amount every year ( or month ). So, make all the premiums the same as the value in C4. Because we still haven't filled in anything in C4, this will show up as $0. Don't worry, we will change that later.

So how much do you owe at the end of the first year? Well, there is the starting $100,000. Add in the interest, and subtract what you paid!

Do the same thing for the other years. You can easily use the copy funtionality in Excel for this, but make sure that the equations have the correct relative behavior ( notice that some of the formulas above have $ signs in the them ). For more details on relative formulas, read up on any introduction to Excel. You should end up with the following numbers.


From the figure above, you can see how fast your loan grows if you don't pay anything. Try putting $20,000 in C4. This is what will happen if you pay $20,000 a year. You end up still owing $17,116 at the end of the fifth year. Now try adjusting the C4 cell to see how much you have to pay each year to get cell C12 to $0. That is how much you should pay every year to pay off this $100,000 loan.

Building Your Own Loan Calculator

That is it for the fundamentals. Now let's do something more fun ( and useful ). I am going to show you how to build your own loan calculator! All you need is MS Excel ( any version will do ), and you're ready to rock and roll. You don't have to be an expert at Excel, as I will try to go through the process in as much detail as I can. If you have difficulty following the steps below due to your comfort level with Excel, you might want to pick up one of the many introductory books on the subject.

Evaluating Cash Flows

Now we are ready to evaluate and compare different cash flows, or multiple payments over time. What does that have to do with real estate? Lots! Taking out a loan for a house means that you will be making multiple payments for years to come. How do those guys actually figure out how much you should pay every month? Also, ever wondered whether it is better to buy than to rent? Sure, there are a whole bunch of calculators and widgets out there on the web, but if you are interested in understanding the science behind real estate, you should start off by understanding the calculations behind them.

Remember, because of interest, we cannot simply sum up the cash amounts over time. Money is money, but money at different points of time is evaluated differently. In order to compare apples to apples, we will have to discount every cash flow to the present. This is also known as taking the present value.

Here is an example - how much are three annual payments of $1000 starting one year from now worth today? Well, from the previous post, we know that the first payment is worth $952.38. Using the formula provided, we can calculate that the second payment is worth $907.03, and the third payment $863.83. Sum them up and you will get $2723.25.

Use this method to evaluate how much your cash flow is worth to you today. You'll be surprised by how much you will overestimate the value if you simply add them up without taking interest into account.

Discounting the Future

Ok, so let us assume that the interest rate is 5%. If we put $1000 in the bank, how much will we have in a year? We will have $1050. Yippee!

So, at an interest rate of 5%, $1000 today is the same as $1050 next year. We can get to this number by doing the calculation below.



Now let's turn the problem around. How much is $1000 next year worth today? At an interest rate of 5%, what is the amount that you will have to put in the bank to get $1000 in a year? Time to brush up on algebra! Assume that you put $X in the bank. You want to solve the following equation below



If we divide both sides by 1.05, we get





Pretty easy, isn't it? This process is called discounting future cash flows. It allows us to bring cash flows onto the same time line so that we can compare different investment options that yield different cash flows.

So the third question is - how much is $1000 in two years worth today? Well, what happens to $X if you put it in the bank for 2 years? Well, you already know what happens in the first year, interest is earned and you end up with



at the end of the first year. So what happens when we leave that amount in the bank for a second year? That's right, we will earn interest on the entire amount! So, by the end of the second year, you will end up with



So in order to figure out what $1000 in two years is worth today, we will have to solve the following equation



There you have it. $X is equal to $907.03. In general, if the interest rate is i%, the value of a P dollars n years in the future is equal to





Understand this formula and remember it. We will use it later on.

Understanding Your Interest

Interest. Now that is a powerful word. A huge portion of finance theory is built on top of this single concept alone. Simply put, interest is how much your money grows over time. Put $1000 in the bank, and in a year, you will have perhaps $1020. That, is because of the interest your $1000 earned, and not because the bank likes you.

But wait! There is more! Interest is also what makes money more valuable now compared to later. Remember that $1000 you put in the bank? It's actually equivalent to $1020 in a year! If given the choice of $1000 today vs $1000 next year, you should always choose $1000 today. Because it is worth more. Because you can put it in the bank, and end up with $1020 next year. So how much more is it worth? By how much interest you can make off of it in a year!

Interest makes our money grow. So interest is good, right? Only if you stay on its good side. Because like everyone with a credit card knows, interest works on debts as well. Unpaid debts accumulate interest, and unchecked debts grow at amazing rates.

What does all of this have to do with real estate? Well, to buy a house, you need a loan. Interest rates will determine how much you pay each month. It also explains why you will end up paying so much more over the lifetime of your loan.