Almost everyone buys a house at some point in their life. Usually the house selection process is subjective: You want to buy a particular house because you like it. While selection of a house is subjective, estimating how much the house is worth is not. In this blog post, I am going to walk you through an objective way to determine the value of a house.

There are two reasons people buy a house: 1. To live in the house, 2. To rent it out (buy a house as an investment). First, I am going to explain valuing the house as an investment. Later, I am going to argue why valuing a house you are going to live in shouldn't be any different from valuing a house as an investment.

## The crux of it

To value any asset, be it a house or a fixed deposit or a share of a publicly traded company, there are only two steps:

Estimate all the cash flows along with their associated timelines for the

*entire lifetime*of that investment. For a house, it is the monthly rents, for a bond, it is the coupon payments and the face value, for shares, it is the dividends or potential dividiendsTranslate all the cash flows to today's money, add them all up

Thats it! The result is the intrinsic value of that asset. in case you don't understand what I mean by "Translating cashflows to today's money", you may want to read up my previous blogs about the *TIme value of money *- __Part1__, __Part2__

## Valuing a house in Bangalore

I want to dive right into an example. Let us consider a house in Bangalore. The cash inflows are the monthly rents. For simplicity, let us not worry about cash outflows such as the yearly house tax and any expense related to repairs. I want to show you the simplest way of estimating a house's value and then talk about all the nuances.

Let us say you expect to get a rent of Rs. 18K this year and you expect the rent to go up by 10% every year. So, on the first year, you will get 18K x 12 months = 216K. On the second year, you will get 216K*(1 + 10%), i.e., 216K*(1.1), on the third year, 216K^(1.1)*(1.1) and so on (simple compounding growth). So the first step of estimating cash flows is over.

The second step of translating all the rents to today's rupees isn't that simple. One could use inflation to "discount" the next year's cash flow and convert it to today's rupees. Inflation in India is around 5.3%. So you could divide this year's (year end's) cash flow by (1 + 5.3%), i.e., (1+0.053), and the cash flow for the year after that by (1.053)*(1.053) and so on (again due to compounding). Overall, the discounted cash flow calculation will look like this:

This is a geometric progression and hence we can convert it to a more compact form:

The variable *n *is lifetime of the house. What is the lifetime of the house? I will let you contemplate that when you are performing your morning duties tomorrow. For now, let us say that it is 50 years. If you substitute *n* = 50, you get the value of the house to be 36.2 million rupees (or 3.62 crores)! That is a superb figure, isn't it? Houses that fetch 18K rupees of monthly rent now can be purchased at 8 million rupees to 10 million rupees (80 lakhs to 1 Crore). In return, you are getting a value that is about 4 times compared to the initial investment. Shouldn't everyone be buying a house in Bangalore?

One of the biggest mistakes we have made in the above calculation is that we have used inflation as the discount rate. As I described in my other blog, * Time value of money* , the discount rate must be commensurate with the risk of the investment; That it should be low for low-risk investment, and high for high-risk investment.

Before we get into calculating it the appropriate discount rate, let us just think what happens if, instead of 5.3%, we use a larger discount rate in our calculations: The following table shows the interest rates and resulting house values.

Note that, for calculating house value when the discount rate is 10%, you cannot use the compact formula (as you will end up with 0/0). Instead, you need to use the original expanded form - It is actually easy because the numerator and denominator rates cancel out in every term and you end up with 216K*50/1.1 = 9.81 million INR.

## Cost of capital

The technical term for the 5.3% we used in the denominator of our formula is "cost of capital". Using just the inflation rate of 5.3% as the cost of capital is only justified for the safest of investments - like, say, a government bond. For all others, we should use a higher cost of capital.

To calculate cost of capital for a house, I am going to assume you will pay for the house partially with your money and partially using a home loan from a bank. We can call your portion as 'equity' and bank portion as 'debt'. So if you pay 40% out-of-pocket and 60% from a bank loan, then the equity is 40% and debt is 60%. We need to calculate cost of capital separately for the debt portion and separately for the equity portion and then combine both.

Calculating cost of capital for debt portion is simple: It is the interest rate at which you get the loan. If you have good credit in India, it will be around 7%. For the equity portion, the idea is to find out how much risk do the market participants see in real estate as an investment. For example, say, some random guy thinks that an investment in a house is riskier than a fixed deposit, but less risky than the stock market. Then find out the returns one can get from a fixed deposit - say, it is 8%. Then find out how much stock returned on an average in the last two decades (BSE or Sensex returns averaged over the last two decades) - say, it is 20%. Now take the average of both - (8% + 20%)/2 = 14%. That, according to that random guy, is the cost of equity for an investment in a house. Keep this as a data point. Collect many such data points from many random guys. The average of all those data points is a good figure to use as the cost of equity.

Generally people use a method called CAPM (google it) to figure out the cost of equity for an asset. For our case, it would involve finding out the average rate of return people of got in the housing market for the last *m *years - where, *m, *is something like 10 years/20 years and then adjusting that figure based on the peculiar aspects of the particular house you are valuing. Doing this, particularly for the Indian housing market is a Dead-on-Arrival suggestion: Buying, selling houses is a opaque process in India due to the black money involved. So instead of CAPM, you can use the method I suggested in the last paragraph.

If you don't even want to use the survey method - probably because you want to do a quick back-of-the-envelope calculation, I suggest an alternative: Tell me what you would have done with your money had you not invested it in a house: If the answer is, "I would have invested it in a fixed deposit", it means, by investing in the house, you will lose the opportunity to invest in a fixed deposit - and hence the rate of return of the fixed deposit becomes the cost of capital of your equity portion (For this reason, cost of capital is also called "opportunity cost"). Of course, here you are implying that a house is just as risky an investment as a fixed deposit. If you underestimate the risk, you will end up overestimating the value of the house. Plus, this will be your opinion - you aren't factoring in what the market opinion is. If your opinion is close of what the average market participant's opinion is, well and good. Otherwise, your valuation will be off.

### Tying it all together

Anyway, let us say that you used *some *method to come with a cost of equity. Let us say it is 20% (something close to stock market amount of risk). Then the combined cost of capital for both the debt and equity portions is simply the weighted average of the individual cost of capitals. I.e., Assuming a 40-60 split for equity and debt, we get:

Cost of capital = (0.4 * 0.20) + (0.6 * 0.07) = 0.074 = 12.2%.

A slightly improved method is to consider the tax advantage related to debt. Suppose, you don't pay income tax on the loan interest payments, then you can use it in the improved cost of capital formula below:

Cost of capital = (0.4 * 0.20) + (0.6 * (1-tax) * 0.07)

So if your income tax slab is 25%, you can use 0.25 for *tax *in the above formula and get:

Cost of capital = (0.4 * 0.20) + (0.6 * (1-0.25) * 0.07) = 0.1094 = 10.94%

Substituting this in our *Present Value *formula, we get,

For *n* = 50, this turns out to be 7.96 million (approx 80L). Still not bad - if you don't consider the nuances (Sorry).

## Nuances

We haven't considered house tax and repair charges per year. We need to subtract them from the rent amount for every year. With age, repair charges will increase - keep that in mind.

Rent growth isn't a given - In fact, after the house crosses a certain years of age, rent might even go down each year, or may become stagnant.

Factoring in these nuances usually mean we cannot use the compact form of the discounted cash flow equation. But we can still use it to arrive at a back-of-the-envelope figure: Suppose we say that the house tax and repair charges will be around 12K this year and will grow at the same rate as the rent, then we should use 202K instead of 216K in our calculation. Considering point 2, say we lower our expected rent growth of 10% to 8% - the result is a disaster: the *Present Value *of the house drops to just 5.08 million rupees (50 L approx).

## FAQ

### What if I sell the house after 10 years? How do I value it then?

Actually it is no different - if the buyer uses intrinsic valuation, from his point-of-view, she will just come up with a value equal to the remainder of the 40 years. Her discounted cash flow valuation will simply have the last 40 terms in the formula you used. A lot of people buy houses without the intention of holding them for their lifetimes. In fact, in Bangalore, most people buy a house not thinking about the cash flows from the rent, but believing that they can sell the house in 10 years and make a 100% profit. And some have indeed done it. But, like professor Aswath Damodaran says, "The problem in investing with the expectation that, when the time comes, there will be a bigger fool to whom you can sell the asset is that you might end up being the biggest fool of all". Basically, hoping that the buyer will not do intrinsic valuation - which is the actual money in that asset - is not a great strategy. Actually, hoping is not a strategy at all.

### What if I am buying a house to live in it?

Suppose you are planning to buy a house A. Imagine a house B that is identical in every way to house A, but is available for rent. If it is identical in every way, then you can take house B on rent and obtain the same utility out of it - or the joy of living in it - as you would from house A. By buying house A, you are saving the rent that you would have otherwise paid for house B So you should value house A the same way you should value house B. In other words, the rent you *don't* pay is just as good a number to use in the calculations as the rent you get from a tenant.

Some people have said something even more interesting - "What if I see a higher value in living in that house than what a typical tenant sees?" - That is, what if I am a guy who would be willing to pay a higher rent (than a typical tenant) for the house I am about to buy, if I were to take it on rent instead? Can I still use the same method for valuing the house? Yes, you can. My explanation here is that, suppose there is a painter whom you really like - When others see just beauty in her paintings, you see much more than that - you see a deep meaning. Damn everyone else, for they are just donkeys who can't appreciate good art. But suppose a painting of hers is available for sale - Even though you may think her painting is worth a million dollars, you would be a complete fool to pay one dollar more than the market price - i.e., the price determined, the very donkeys who you think can't appreciate that art. If you can own the art by paying, say, a hundred dollars, you wouldn't willingly pay a million dollars, even if you think it is worth it, right? (If you do, that wouldn't be *buying. *It would just be charity).

### If my estimate is much lower than the market value of the house, am I wrong or is everyone else wrong?

Either may be true. Remember that, in the calculation, you are using a lot of estimates: The rent you will get this year, how much it will grow year-on-year, how much is the cost of capital etc. There is a chance that your estimates are wrong. But equally, there is a chance that others are estimating them incorrectly. In fact, my bet, at least as far as housing market in Bangalore is concerned, is that most of the market participants don't use any type of value estimation at all.

At the end of the day, I prefer to use inaccurate estimates (my best guess) rather than use no estimates at all and accept the market price. If I accept the market price as the correct value of the house without doing any valuation on my own, I would be either implying that people in general aren't stupid, or if they are indeed stupid, they will remain stupid until the time comes when I will sell the property and see the returns. Both are dangerous suggestions.

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