For simplicity, we will assume that the business in question will earn $10,000 each year for the next thirty-plus years.
Intuitively, we know that collecting $10,000 each year for the next thirty years is not the same as receiving all $300,000 today.
Let us analyse and see what thirty-plus years of earning $10,000 per year are really worth to us today, using a discount rate of 6%.
Present value
= Annual Cash Flow / Discount rate
= $10,000 / 0.06
= $166,667
(In reality, we should look for how much cash we receive from the business over its lifetime. For the purposes in this post, we will assume that earnings are a good approximation for cash received.)
So, earning $10,000 a year for the next thirty-plus years turns out to be worth about $166,667 today.
We have just figured out something incredibly important.
A business guaranteed to earn us $10,000 each year for the next thirty-plus years or so, is worth the same as having $166,667 cash in our pocket today!
If we could be guaranteed that all of our assumptions were correct and someone offered to sell us the company for $80,000, should we do it? If someone offered to give us $166,667 right now in exchange for $80,000, should we do it?
Given all of our assumptions, the answer is easy: of course we should do it!
This is an incredibly important concept.
If we can really figure out the value of a business, investing becomes very simple!
The secret to successful investing is to figure out the value of something and then - pay a lot less!
In fact, it couldn't be simpler: $166,667 is a lot more than $80,000.
In practice, predicting so far into the future is pretty hard to do.
Are you really going to trust my predictions about what earnings will be over the next thirty years?
But will earnings actually shrink over those years?
Will they grow?
Will the company even be around in another thirty years?
In practice, predicting so far into the future is pretty hard to do. In addition, many businesses are actually more complicated.
In fact, forget thirty years - it turns out that Wall Street analysts are actually pretty bad at predicting earnings for even the next quarter or the next year.
You will probably pay less for those estimated earnings than if they were guaranteed.
Since no one rally knows for sure what earnings will be over the next thirty-plus years, whatever we use for estimated earnings during that time is just going to be a guess. Even if this guess is made by a very smart, informed "expert", it will still be a guess.
In practice, investors discount the price they will pay for future earnings that are based only on estimates.
If there is no guarantee that you will actually collect that $10,000 after the first year of owning the business, you will probably pay less for those earnings than if they were guaranteed.
In the above example, where next year's earnings of $10,000 were guaranteed, we discounted that payment by 6%, reflecting the fact that we had to wait a year to collect our $10,000. Now, with only an estimated $10,000 coming in at the end of the first year, we will pay less.
How much less?
That's not exactly clear, but we would certainly discount that hoped-for $10,000 by more than the 6% we used when the $10,000 was guaranteed - maybe we'd use a discount of 8% or 10% or 12%, or even more. (the amount of our discount would reflect in part how confident we were in our earnings estimate).
But when we apply that higher discount to the next thirty-plus years of earnings estimates, that's when things really start to get silly (yes, it's true, math can be hilarious).
Value of the Company
At 6% discount rate
$10,000 /0.06 = $166,667
At 8% discount rate
$10,000 / 0.08 = $125,000
At 12% discount rate
$10,000 / 0.12 = $ 83,333
As it turns out, using a 12% discount rate, the value of the company is only $83,000. We are starting to get in trouble! It is no longer so obvious that a purchase price of $80,000 is such a bargain!
Figuring out the right discount rate isn't our only problem, we also have to estimate earnings.
What is crystal clear, however, is that using different discount rates for our estimated earnings can lead to wildly different results when we try to value a business. But figuring out the right discount rate isn't our only problem. For simplicity, we have made some other assumptions that don't really hold up in the real world.
For instance, as you might intuitively guess, most companies don't earn the same amount each year for thirty straight years. Also, many businesses grow their earnings over time, while others due to competition, a bad product, or a poor business plan, see their earnings shrink or even disappear over the years.
Let us see how funny the math gets when we try to value a business using not only different estimates for discount rates but we throw on top of that some different guesses for future earnings growth rates!
Value of the Business
At 4% growth rate, 8% discount rate
$10,000 / (0.08 - 0.04) = $250,000
At 4% growth rate, 12% discount rate
$10,000 / (0.12 - 0.04) = $125,000
At 6% growth rate, 8% discount rate
$10,000 / (0.08 - 0.06) = $500,000.
Annual Cash Flow / (Discount Rate - Growth Rate) = Present Value
According to finance theory and logic, the value of a business should equal the sum of all of the earnings that we expect to collect from that business over its lifetime (discounted back to a value in today's dollars based upon how long it will take us to collect those earnings and how risky we believe our estimates of future earnings to be).
Will earnings grow at 2%, 4%, 6% or not at all? Is the right discount rate 8%, 105, 12%, or some other number?
The math says that small changes in estimated growth rates or discount rates or both can end up making huge differences in what value we come up with!
At 2% growth rate, 12% discount rate
$10,000 / (0.12 - 0.02) = $100,000
At 5% growth rate, 8% discount rate
$10,000 / (0.08 - 0.05) = $333,333
Annual Cash Flow / (Discount Rate - Growth Rate) = Present Value
Which numbers are right?
It is incredibly hard to know. Whose estimates of earnings over the next thirty-plus years should we trust? What discount rate is the right one to use?
The secret to successful investing is to figure out the value of something and then - pay a lot less.
How are we going to figure out value? How can anyone? Do we have the answer yet? Hopefully, we have learned some very valuable lessons even if we cannot answer them yet.
Summary:
1. The secret to successful investing is to figure out the value of something and then pay a lot less!
2. The value of a business is equal to the sum of all of the earnings we expect to collect from that business over its lifetime (discounted back to a value in today's dollars). Earnings over the next twenty or thirty years are where most of this value comes from. Earnings from next quarter or next year represent only a tiny portion of this value.
3. The calculation of value in #2 above is based on guesses. Small changes in our guesses about future earnings over the next thirty-plus years will result in wildly different estimates of value for our business. Small changes in our guesses about the proper rate to discount those earnings back into today's dollars will also result in wildly different estimates of value for our business. Small changes in both will drive us crazy.
4. If our estimate of value can change dramatically with even small changes in our guesses about the proper earnings growth rate to use or the proper discount rate, how meaningful can the estimates of value made by "experts" really be?
5. The answer to #4 above is - "not very."
Additional notes:
These concepts involve a discussion of the time value of money and discounted cash flow.
In reality, we should look for how much cash we receive from the business over its lifetime. For the above purposes, we will assume that earnings are a good approximation for cash received.
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