How To Calculate Return On Investment

The Gotham Gal and I make a fair number of non-tech angel investments. Things like media, food products, restaurants, music, local real estate, local businesses. In these investments we are usually backing an entrepreneur we’ve gotten to know who delivers products to the market that we use and love. The Gotham Gal runs this part of our investment portfolio with some involvement by me.

As I look over the business plans and projections that these entrepreneurs share with us, one thing I constantly see is a lack of sophistication in calculating the investor’s return.

Here’s the typical presentation I see:

The entrepreneur needs $400k to start the business, believes he/she can return to the investors $100k per year, and therefore will generate a 25% return on investment. That is correct if the business lasts forever and produces $100k for the investors year after year after year.

But many businesses, probably most businesses, have a finite life. A restaurant may have a few good years but then lose its clientele and go out of business. A media product might do well for a decade but then lose its way and fold.

And most businesses are unlikely to produce exactly $100k every year to the investors. Some businesses will grow the profits year after year. Others might see the profits decline as the business matures and heads out of business.

So the proper way to calculate a return is using the “cash flow method”. Here’s how you do it.

1) Get a spreadsheet, excel will do, although increasingly I recommend google docs spreadsheet because it’s simpler to share with others.

2) Lay out along a single row a number of years. I would suggest ten years to start.

3) In the first year show the total investment required as a negative number (because the investors are sending their money to you).

4) In the first through tenth years, show the returns to the investors (after your share). This should be a positive number.

5) Then add those two rows together to get a “net cash flow” number.

6) Sum up the totals of all ten years to get total money in, total money back, and net profit.

7) Then calculate two numbers. The “multiple” is the total money back divided by the total money in. And then using the “IRR” function, calculate an annual return number.

Here’s what it should look like:

Here’s a link to google docs where  I’ve posted this example. It is public so everyone can play around with it and see how the formulas work.

It’s worth looking for a minute at the theoretical example. The investors put in $400k, get $100k back for four years in a row (which gets them their money back), but then the business declines and eventually goes out of business in its seventh year. The annual rate of return on the $400k turns out to be 14% and the total multiple is 1.3x.

That’s not a bad outcome for a personal investment in a local business you want to support. It sure beats the returns you’ll get on a money market fund. But it is not a 25% return and should not be marketed as such.

I hope this helps. You don’t need to get a finance MBA to be able to do this kind of thing. It’s actually not that hard once you do it a few times.

The Present Value of Future Cash Flows

My friend Pravin sent me an email last week after my “How To Calculate A Return On Investment” post. He said:

I wish there was a class that I could take that would teach me how to properly research stocks/companies for investment purposes and how that could be made into a private tutoring business. It’d be for people like me, people who didn’t go to school for business but still are interested in understanding all the jargon, methods of investing, etc and how to apply it to a buy and hold strategy.

Pravin then went on to say that the post I wrote was exactly the kind of thing he was looking for and that he’d like to see me do more of it. So with that preface, I’d like to announce a new series here at AVC. I’m calling it “MBA Mondays”. Every monday I’ll write a post that is about a topic I learned in business school. I’ll keep it dead simple (many people thought my ROI post last week was too simple). And I’ll try to connect it to some real world experience.

I’ll start with the topic Pravin wanted some help with: how to value stocks, what they are worth today, and what they could be worth in the future. This topic will take weeks of MBA Mondays to work through but we’ll start with a fundamental concept, the present value of future cash flows.

I was taught, and I believe with all my head and heart, that companies are worth the “present value” of “future cash flows”. What that means is if you could know with certainty the exact amount of cash earnings that the company will produce from now until eternity, you could lay those cash flows out and then using some interest rate that reflects the time value of money, you could calculate what you’d pay today for those future cash flows.

Let’s make it really simple. You want to buy the apartment next to you for investment purposes. It rents for $1000/month. It costs $200/month to maintain. So it produces $800/month of “cash flow”. Let’s leave aside inflation, rent increases, cost increases, etc and assume for this post that it will always produce $800/month of cash flow.

And let’s say that you will accept a 10% annual return on your investment. There are a multitude of reasons why you’ll accept different interest rates for different investments, but we’ll just use 10% for this one.

Once you know the cash flow ($800/month) and the interest rate (also called the “discount rate”), you can calculate present value. And this example is as easy as it gets because the cash flow doesn’t change and the interest rate is 10%.

The annual cash flow is $9,600 (12 x $800) and if you want to earn 10% on your money every year, you can pay $96,000 for the apartment. In order to check the math, let’s calculate 10% of $96,000. That’s $9,600 per year.

In practice, it is never this simple. Cash flows will vary year after year. You’ll have to lay them out in a spreadsheet and do a present value analysis. We’ll do that next week.

But it is the principle here that is important. Companies (and other investments) are worth the “present value” of all the cash you’ll earn from them in the future. You can’t just add up all that cash because a dollar tomorrow (or ten years from now) is worth less than a dollar you have in your pocket. So you need to “discount” the future cash flows by an acceptable rate of interest.

That basic concept is the bedrock of all valuation concepts in finance. It can get incredibly complex, way beyond my ability to calculate or even explain. But you have to understand this concept before you can go further. I hope you do. Next week we’ll look at using spreadsheets to calculate present values.

The Time Value of Money

Last week, I posted about The Present Value Of Future Cash Flows and in the comments Pascal-Emmanuel Gobry wrote:

That being said, before even covering NPV, I would have first talked about the time value of money. To me, time value of money is one of the top 3 concepts that blew my mind in business school and that should be common knowledge. When you think about it, all of finance, but also much of business, is underpinned by that. Once you understand time value of money, you understand opportunity costs, you understand sunk costs, you just view the world in a whole different light.

PEG is right. We have to talk about the Time Value Of Money and it was a mistake to dive into concepts like Present Value and Discount Rates before doing that. So we’ll hit the rewind button and go back to the start. Here it goes.

Money today is generally worth more than money tomorrow. As another commenter to last week’s post put it “you can’t buy beer tonight with next year’s earnings”. Money in your pocket, cash in hand, is worth more than cash that you don’t actually have in hand. If you think about it that simply, everyone can agree that they’d rather have the cash in hand than the promise of the same amount at some later day.

And interest rates are used to calculate exactly how much more the money is worth today than tomorrow. Let’s say that you’d take $900 today instead of $1000 exactly a year from now. That means you’d accept a 11.1% “discount rate” on that transaction. I calculated that as follows:

1) I calculated how much of a “discount” you would take in order to get the money today versus next year. That is $1000 less $900, or $100

2) I then divided the discount by the amount you’d take today. That is $100/$900, which is 11.1%.

This transaction could be modeled out the other way. Let’s say you are willing to loan a friend $900 and you agree that he’ll pay you an interest rate of 11.1%. You multiply $900 times 11.1%, you get $100 of total interest, and add that to the $900 and calculate that he’ll pay you back $1000 a year from now.

As you can tell from the way I talked about them, interest rates and discount rates are generally the same thing. There are technical differences, but both represent a rate of increase in the time value of money.

So if the interest rate describes the time value of money, then the higher it is, the more valuable money is in your hands and the less valuable money is down the road.

There are multiple reasons that money can be more valuable today than tomorrow. Let’s talk about two of them.

1) Inflation – This is a complicated topic that we are not going to get into in detail here. But I need to at least mention it. When prices of things rise faster than they should, we call that inflation. It can be caused by a number of things, most often when the supply of money is rising faster than is sustainable. But the important thing to note is that if a house that costs $100,000 today is going to cost $120,000 next year, that represents 20% inflation and you’d want to earn 20% on your money every year to compensate you for that inflation. You’d want a 20% interest rate on your cash to be compensated for that inflation.

2) Risk – If your money is in a federally guaranteed bank deposit for a year, you might accept 2% interest on it. If it is invested in your friend’s startup, you might want a double on your money in a year. Why the difference between a 2% interest rate and a 100% interest rate? Risk. You know you are getting the money in the bank back. You are pretty sure you aren’t getting the money back that you invested in your friend’s startup and want to get a lot back if it works out.

So let’s deconstruct interest rates a bit to parse these different reasons out of them.

Let’s say the current rate of interest on a one year treasury bill (a note sold by the US Gov’t that is federally guaranteed) is paying a rate of interest of 3%. That is an important rate to pay attention to. Because it is a one year interest rate on a risk free instrument (assuming that the US Gov’t is solvent and always will be). We will assume for now that is true. So the “risk free rate” is 3%. That is the rate that the “market” says we should be accepting for a one year instrument with no risk.

Now let’s take inflation into account. If the Consumer Price Index (the CPI) says that costs are rising 2.5% year over year, then we can say that the one year inflation rate is 2.5%. It can get a lot more complicated than this, but many real estate leases use the CPI so we can use it too. If you subtract the inflation rate from the risk free rate, you get something called the “real interest rate”. In our example, that would be 0.5% (3% minus 2.5%). And we call the 3% rate, the “nominal rate”.

Now let’s take risk into account. Let’s say you can find a corporate bond in the bond market that is coming due next year and will pay $1000 and it is trading for $900 right now. We know from the example that we started with that it is “paying” a discount rate of 11.1% for the next year. If we subtract the 3% risk free rate of interest from the 11.1%, we can determine that market is demanding a “risk premium” of 8.1% over the risk free rate for this bond. That means that not everyone thinks that this company is going to be able to pay back the bond in full, but most people do.

Ok, so hopefully you’ll see that interest rates and discount rates have components to them. In its simplest form, and interest rate is composed of the risk free rate plus an inflation premium plus a risk premium. In our examples, the risk free “real” interest rate is 0.5%, the inflation premium is 2.5%, and the risk premium on the corporate bond is 8.1%. Add all of those together, and you get the 11.1% rate that is the discount rate the corporate bond trades at in the markets.

Which leads me to my final point. Markets set rates. Banks don’t and governments don’t. Banks and governments certainly impact rates and governments can do a lot to impact rates and they do all the time. But at the end of the day it is you and me and it is the traders, both speculators and hedgers, who determine how much of a discount we’ll accept to get our money now and how much interest we’ll want to wait another year. It is the sum total of all of these transactions that create the market and the market sets rates and they change every second and always will (at least in a capitalist system).

That was tough to do in a blog post. It’s a very simple concept but very powerful and as Pascal-Emmanuel said, it is fundamental to all of finance. I hope I explained it well. It’s important to understand this one.

It’s time for MBA Mondays again. For the third week in a row, the topic of the post has been suggested by a reader. Last week, Elia Freedman wrote:

“A suggestion for your next post. The logical follow-on is to explain the second half of the TVM (time value of money), which is compounding interest.”

Before I address the issue of compounding interest, I’d like to recognize two things about the MBA Monday series. The first is that each post has a very rich comment thread attached to it. If you are seriously interested in learning this stuff, you would be well served to take the time to read the comments and the replies to them, including mine. The second is that the readers are building the curriculum for me. Each post has resulted in at least one suggestion for the next week’s post. I dove into MBA Mondays without thinking through the logical progression of topics. At this point, I’m just going to run with whatever people suggest and try to assemble it on the fly. It’s working well so far. So if you have a suggestion for next week’s topic, or any topic, please leave a comment.

Last week, I described interest as the rate of change in the time value of money. And we broke interest rates down into the real rate, the inflation factor, and the risk factor. And we calculated that if you invested $900 today at an 11.1% rate of interest, you’d end up with $1000 a year from now.

But what happens if you wait a few years to get your money back and receive annual interest payments along the way? Let’s say you invest the same $900, receive $100 each year for four years, and then in the last year, you receive $1000 (your $900 back plus the final year’s $100 interest payment).

There are two scenarios here and they depend on what you do with the annual interest payments.

In the first scenario, you pocket the cash and do something else with it. In that scenario, you will realize the 11.1% rate of interest that you would have realized had you taken the $1000 one year later. It’s basically the same deal, just with a longer time horizon. And your total proceeds on your $900 investment are $1400 (your $900 return of “principal” plus five $100 interest payments).

In the second scenario, you reinvest the interest payments at 11.1% each year and take a final payment in year five. If you reinvest each interest payment at 11.1% interest, at the end of year five, you will receive $1524 as your final payment. Notice that the total proceeds in this scenario are $124 higher than in the other scenario. That is because you reinvested the interest payments instead of pocketing them.

Both scenarios produce a “rate of return” of 11.1%. If you look at this google spreadsheet, you can see how these two scenarios map out. And you can see the calculation of total profit and “internal rate of return”.

The fact that you make a larger profit on one versus the other at the same “rate of interest” shows the power of compounding interest. It really helps if you reinvest your interest payments instead of pocketing them. While $124 over five years doesn’t seem like much, let’s look at the power of compounding interest over a longer horizon.

Let’s say you inherit $100,000 around the time you graduate from college. Instead of spending it on something, you decide to invest it for your retirement 45 years later. If you invest it at the 11.1% rate of interest that we’ve been using, the differences between pocketing the $11,100 you’d get each year and reinvesting it are HUGE.

If you pocket the $11,000 of interest each year, you will receive $599,500 on your $100,000 investment over 45 years.

But if you reinvest the $11,000 of interest each year at 11.1% interest, you will receive $11.4 million dollars when you retire. That’s right. $11.4 million dollars versus $599,500. That is the power of compounding interest over a long period of time.

You can see how this models out in this google spreadsheet (sheets two and three).

Now let’s tie this issue to startups and venture capital. Venture capital investments are often held for a fairly long time. I am currently serving on several boards of companies that my prior firm, Flatiron Partners, invested in during 1999 and 2000. Our hold periods for these investments are into their second decade. Of course not every venture capital investment lasts a decade or more. But the average hold period for a venture capital investment tends to be about seven or eight years.

And during those seven to eight years, there are no annual interest payments. So when you calculate the rate of return on the investment, the spreadsheet looks like this. It’s a compound interest situation.

If you go back to the $100,000 over 45 years example, you’ll see that a return of 114x your money over 45 years produces the same “return” as 6x your money with annual interest payments.

The differences are not as great over seven or eight years but they are made greater by virtue of the fact that VCs seek to make 40-50% annual rates of return on their capital. If you read last week’s post, you’ll know that comes from the risk factor involved. The more risk an investment has, the higher rate of return an investor will require on their money in a successful outcome.

If you want to generate a 50% rate of return compounded over eight years on $100,000, you will need to return $2.562 million, or 25.6x your investment. See this google spreadsheet (sheet 4) for the details.

The good news is that most venture capital investments are made over time, not all at once in the first year. So the “hold periods” on the later rounds are not as long and make this math a bit easier on everyone involved (maybe a topic for next week or some other time?).

But as you can see, compounding interest over any length of time increases significantly the amount of money you need to return in order to pay the same rate of return as a security with annual interest payments. There are two big takeaways here. The first is if you are an investor, you should reinvest your interest payments instead of spending them. It makes a huge difference on the outcome of your investment. The second is if you are an entrepreneur, you should take as little money as you can at the start and always understand that your investors are seeking a return and that the time value of money compounds and makes your job as the producer of that return particularly hard.