When I was starting out trying to educate myself on investing, I kept hearing the same sound advice to look for companies that were trading for less than they were really worth.

That sounded like a great idea. I liked it. But I (initially) had one problem. How was I supposed to know what a business was worth?

Well that’s what this section is for. My goal here is to provide an oversight (largely for beginners or those unfamiliar with the process) of valuation. I hope that after reading this, those unfamiliar or uncomfortable with the process of figuring out what a business is worth can feel a bit more confident. So, here goes.

Book Value (Liquidation Value)

Imagine you own your own small business (all 100% of it). Let’s assume first that you’re a mediocre businessperson and you figure your business will break even every year (clearly, you and I both know that this WAY underestimates your true potential, but just for demonstration’s sake, stay with me). Your business has $1,000 in the bank and $500 worth of equipment (and let’s assume that it will not go down in value, ordepreciate, in financial lingo). Someone comes to you and offers you $1,200 to sell the business. Will you sell it?

If you’re at all rational, you shouldn’t. You know that with $1,000 in the bank and $500 of equipment your business has to be worth at least $1500 (unless you’re the type who likes to give away dollar bills for eighty cents. I’m not that type). That is, if you close the business, take the cash, and sell the equipment, you’d be better off than selling it to the miser who offered you $1200.

But that’s easy. You knew that.

Now let’s assume that in addition to the $1,000 in the bank and $500 of equipment, you took out a loan in the amount of $600 to finance your business. Would you sell it for $1200 now?

You should definitely think long and hard about it. The $600 loan (ignoring the fact that you’ll have to pay interest on it, which means you WON’T be breaking even anymore) means the business has $1500 and owes $600, for a net “book value” of ($1500-$600) = $900. Since the business won’t be earning any money, this is probably a good indication of what it’s worth.

This is the first and most basic metric of business valuation – book value (or shareholder equity or liquidation value). Simply put, a business with money in the bank (i.e. assets) net of all that it owes (i.e. liabilities) is worth at least its book value (assets minus liabilities). This, of course, is assuming that the business will not make profits.

But what if it does?

Earnings Power Value

Now let’s assume that your business is profitable and makes $200 per year in profits. You expect it to make $200 every year, so that profits neither go up nor down. You are certain that this will be the case, so there is no risk. The same miser comes to you again and this time offers you $2000 for the business. Will you sell it?

Well, that depends. Because you know your business is going to earn $200 every year without risk, you need to know the opportunity cost of your business’s stream of cash. That’s because by selling the business, you forego the $200 per year in cash flow for a lump sum payment. So the valuation question becomes: what is a fair value for that lump sum payment?

Being a savvy businessperson (I told you that you weren’t mediocre…), you tell the businessman that, with interest rates at 5%, his $2000 can earn you $2000*5% = $100 per year. That’s way below the $200 you earn from your business, so you again tell the miser to take a hike. You know that you should get at least $X*.05 = $200, or $X = $200/.05 = $4000 for your business.

Now let’s say that interest rates were really 4%. What is the business worth now? Using the same logic, $200/.04 = $5000. Because the opportunity cost of selling your business went up (i.e. interest rates are lower), you demand a higher payment for the business and its profitability.

In summary, this (in its simplistic form) is a valuation method that finds a fair value of a constant earnings stream by sizing up opportunity costs.

But it’s not very realistic. In the real world, business’ earnings either grow or fall, inherent risks exist in the business, and there is no certainty. And because it costs money to make money, you’ve got to consider what you paid for that money (i.e. capital).

So now what?

Discounted Cash Flow (DCF) – Bringing it all together

Before starting this, I want to make one thing – an integral concept calledpresent value – clear. As we started discussing above, opportunity cost is an important (if not the most important) economic factor in investing. So let’s start with this.

If you were offered $1 today versus $1 tomorrow, which would you choose?

Duh. $1 today. Everyone intuitively understands this concept. But whywould you take it today? Because by foregoing it for the same $1 tomorrow, you give up spending it, investing it, or otherwise enjoying it (swimming in it, perhaps?). Call it impatience, call it prudence, call it whatever: a bird in the hand is worth two in the bush.

Now, what if I offered you $0.90 today versus $1.00 tomorrow. Would you take it?

That’s a bit harder, but let’s assume that interest rates (your opportunity cost) are 10%. That means you can take the $1 today and put it in the bank to get ($0.90 + $0.90*10%), or simply $0.90*(1+0.1) = $0.99. So $0.90 today is really worth $0.99 tomorrow. So you should probably take the $1.00 tomorrow.

An easier way to look at this is to simply rearrange the equation to figure out what the dollar tomorrow is worth today (rather than what $1 today is worth tomorrow). This is the so called Present Value (PV). So let’s do that:

If $PV*(1+interest rate) = $1 tomorrow, then PV = $1/(1+interest rate).

More generally, PV = FV/(1+r) where r = the interest rate, opportunity cost, etc. and FV is the Future Value (in this example, $1).

Easy enough.

Now, let’s extend this to beyond just the value of a dollar tomorrow. What is a dollar the day after tomorrow worth? If you guessed that it should be worth even less than a dollar tomorrow, you’re spot on. But how much is it worth?

Well, you know that you can put money in the bank and earn interest tomorrow, and then that interest will earn interest on the next day. More precisely, with interest rates of r, $1 today = (1+r)*(1+r)*$1 tomorrow. Rearranging the equation generally, we see that PV*(1+r)*(1+r)=FV, or PV = FV/(1+r)^2.

Not too bad. Obviously, because in three days from now, interest earns interest earns interest, etc., PV=FV/(1+r)^3. Thus, in the most general form PV=FV/(1+r)^t, where t=time of the future payment.

Armed with the notion of Present Value, we can now weigh all opportunities against one another, and determine what real businesses, in the real world, are worth. So, we go to the Discounted Cash Flow model, the Holy Grail of valuation.

Say it turns out (not surprisingly) that you’ve built a pretty good business, and your $200 stream of earnings from above will grow at 4% forever, risk free. What’s it worth, assuming interest rates of 10%?

We know that next year, the business will earn $200*(1.04) = $208, in two years, $200*(1.04)^2 = $216.32, etc. We can take those earnings, anddiscount them by the interest rate (exactly as we did above). After figuring out what each years earning stream is worth today, we can sum up the present values, and arrive at a value for the entire growing earning stream (or, simply, the business).

Here:

[200*1.04]/1.10 + [200*1.04^2]/1.10^2 + [200*1.04^3]/1.10^3 +… and on and on.

That’s all well and good, but how do we sum that? Luckily a neat algebraic trick (the details of which, for now, I’ll spare you), shows that

Value of Business (or PV of cash flows) = $200/[10%-4%] = $3333.33. This short trick, more generally, is that PV=Current CashFlow/[r-g], where g is the growth rate.

Pretty useful stuff.

But now, let’s make life a bit more complicated (don’t worry, it’s not too bad). Let’s assume (not surprisingly) that you’ve built a hell of a business, and that you expect your business to grow earnings at 20% for the next 10 years, and 5% thereafter. Now what’s it worth?

Well, we use pretty much the same methods, but this time divide up the model into the part in which earnings grow at 20% and the part where earnings grow at a constant rate (called the continuing value, which, as you may have guessed, is exactly the same logic that we used above).

Here goes:

In the first 10 years:

Sum of PVs = [200*(1+20%)]/(1+10%)+[200*1.2^2]/(1+10%)^2+…+[200*1.2^10]/(1+10%)^10

After doing the work (the easiest way is on excel), we find that:

PV(first 10 years)=$3329.20

Now, using the neat trick from above, the continuing value after this big growth period is found by figuring out the earnings in year 11 (discounted to the present as done above), and dividing by the continuing growth rate of 5% minus the discount rate of 10%. So (now, follow this because it looks messy, but isn’t too bad:

{[200*1.2^10+200*1.05]/(1.1^10)}/(10%-5%)=$10,026.17

By summing the $3329.20 and $10,026.17 we arrive at a total value of the business of $13,355.40.

Now you can really tell the miser to hit the road.

Naturally, this framework is identical to the methods of valuing stocks. Stocks are small pieces of businesses, so figuring out what they are worth is simply a matter of figuring out what the underlying business is worth. This is done by discounting reasonable estimates of the business’s future cash flows back to the present. It’s a simple process, but not easy. It involves the use of many inputs (estimates of earnings, a discount rate) that can lead to wildly different values.

So you, as an investor, are looking to be the miser: trying to buy businesses for way less than they’re worth. Naturally, your inputs will never be perfect, and at any given time no one knows the exact value of a business. So to compensate, you should demand a margin of safety, so that, even if you’re not exactly right, you have a cushion to work with. If you think a business is worth $50 a share and it sells for $45, that’s probably not enough wiggle room.

But you knew that.

All of this, in short, is an overview of the most important valuation methods. I’ll continue adding to this section as time goes on, with more detailed descriptions of the methods, as well as posing some problems with the models and some more food for thought.

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