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Explaining Discount Rates

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February 11, 2008 – Comments (0)

This post is from Old School Value

Discount rates and the concept of discounting can be very confusing to understand at first. I talk from experience. For a budding investor, trying to understand future value and then discounting to get a present value can be quite tricky. So I'll try to provide a simple explanation.. (please let me know if you have a simpler way of explaining it)

Let's start with a quote from Buffett "The value of any stock, bond or business today is determined by the cash inflows and outflows - discounted at an appropriate interest rate - that can be expected to occur during the remaining life of the asset."


The Future Value Of A Company
We calculate the future value of a company by predicting its future cash generation and then adding the total sum of the cash generated throughout the life of the business. This requires that we find a growth rate and apply it to the companys free cash flow.

To illustrate, let's assume a companys latest fiscal filing revealed $100 in free cash in 2008. With a growth rate of 10%, we predict that the company will be able to generate $110 in free cash in 2009 and $121 in 2010 and so on for the next 10 years. The total sum of the free cash over 10 years comes out to $1,753. That is, we expect the company to pump out $1,753 over 10 years.


The Present Value Of A Company
But the sum of $1,753 over 10 years is not worth $1,753 today. There is time value in money. I would not want to invest $1,753 today in one lump sum such that I will receive $1,753 over 10 years. That will give me a 0% investment return. I want to buy that $1,753 for an amount where I will be getting a satisfactory return out of my investment.

When people pool their money together for a real estate investment, they may pay $100,000 today to get a piece of a $1,000,000 investment in a resort. In this example, they are assuming that $1,000,000 is worth $100,000 today.

Therefore, we must figure out how much we are willing to pay today, in order to receive $1,753 over the 10 years.

Discount It Back
There is no hard and fast rule for choosing a discount rate. Using a high discount rate to discount the future cash just means you are willing to pay less today for the future cash and vice versa.

Do understand that "You can’t compensate for risk by using a high discount rate."
If 15% was used to discount $1,753, the investor would be only willing to pay $1,524 in todays money for $1,753. Using a 9% discount rate would give a value of $1,608 for the $1,753. We can see that using a high discount rate will give a lower valuation than a lower discount rate.

But Buffett Used The 10 Year Treasury Rate!
Yes, he did use the treasury rate. But he was using a rate that was equal to a risk free return. Had he put his money in 10 year treasury bonds, he would have earned around 8.85% at that time without any risk. If we were to do the same and use a risk free rate treasury rate today, we would only be discounting the future value by around 3%. Do you want an annual return of 3% from your portfolio? Buffett's choice to discount by the treasury rate was his minimum required return. He also used the treasury rate as a measuring stick for all businesses, rather than assigning a different rate for different businesses.

"In order to calculate intrinsic value, you take those cash flows that you expect to be generated and you discount them back to their present value - in our case, at the long-term Treasury rate. And that discount rate doesn't pay you as high a rate as it needs to. But you can use the resulting present value figure that you get by discounting your cash flows back at the long-term Treasury rate as a common yardstick just to have a standard of measurement across all businesses."

So What Is A Good Rate?
Why do I choose 15%? Like Buffett, I have a minimum return rate that I want and that happens to be 15%. I could seek 20% or even 30% but that will just make my search so much harder and limited because I will be trying to buy $1,753 for $1,349. (It may look feasible when the numbers are small, but when we are talking in billions, it comes out the same as buying $17.5 billion for $13.4 billion today. A difference of nearly $5 billion!)

In my example of Apple I used a 9% discount rate. Why not 15%?

"If we thought we were getting a stream of cash over the thirty years that we felt extremely certain about, we'd use a discount rate that would be somewhat less than if it were one where we expected surprises or where we thought there were a greater possibility of surprises."
Since AAPL is a cash cow, has a good business with a fairly wide moat and not expected to go bankrupt, I used a 9% rate. Had I examined WalMart, Coca Cola, Johnson & Johnson or Microsoft, I would also have chosen a rate of 9% since historical data provides evidence of steady predictable cash growth and so future estimates would be much more predictable than the likes of an IPO or startup.

However, the important aspect is not deciding upon a discount rate, but in being logical and reasonable about cash projections.


"Don't use different discount rates for different businesses...it doesn't really matter what rate you use as long as you are being intellectually honest and conservative about future cash flows."


Don't Forget Margin Of Safety
Whatever rate you choose, never forget to apply a margin of safety because no one can accurately predict the future. But note that a high discount rate may warrant a lower margin of safety but that is up to the investor. Personally, I use a 15% discount rate with a 50% margin of safety. For a majority of my investments, I want a minimum of 15% annual return and I want to to be able to buy $1 for 50c, thus the 50% margin of safety. This eliminates 95% of investment opportunities but it also reduces my risk of losing a lot of money in 95% of my investmetns. However, for huge, stable institutions, I tend to use 9% with 50% margin of safety.

Final Thoughts
Don't justify the purchase of a company just because it fits the numbers. Don't fool yourself into believing that a cheap company will yield good returns. A bad company is a bad investment no matter what price it is.

I love how Charlie Munger explains that
"a piece of t.u.rd in a bowl of raisins is still a piece of t.u.rd"and
"there is no greater fool than yourself, and you are the easiest person to fool."
Let's not fool ourselves. Exercise your options. Not a call or a put, but a "NO".

Disclaimer
I hold no shares in any of the companies mentioned above.

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