How are we going to figure out value? How can anyone? Do we have the answer yet?

Valuing a company you are investing into.

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.  

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.   

In practice, predicting so far into the future is pretty hard to do.  

You will probably pay less for those estimated earnings than if they were guaranteed.

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).  

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.  

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.

Figuring out the right discount rate isn't our only problem, we also have to estimate earnings. 

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.