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 Discount 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 turd in a bowl of raisins is still a piece of turd”
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.
August 28th, 2008 at 8:23 pm
Not entirely sure why anyone would use a 15% discount rate instead of just using the risk free rate, namely 3 or 4% to compensate interest rates and basically 4% for 10 year bond treasury yield…hence 8%’ish.
The cash flow is where you put your return, not the discount rate?
Simply (say you’re buying 2 years worth of cash flow to keep this short)…
1st yr – $2000 (after analyzing the business and its operations and its environment, you think it’s reasonable that they will grow 15% in the second year)
Fine, PUT IT IN THE CASH FLOW. ($2000 x 15% = $300)
2nd yr – $2300
NOW, discount that year back by the 8% risk free rate ($2300 / (1.08)^2) = $1971.87 (rounded down)
So Year 1 and 2 cash flow today is worth $2000 + $1971.87 = $3971.87
Arguably, the problem is people don’t know how to do what they’re trying to do. Probably, you ought to be buying a business you can actually know how the cash flow is going to look like the future. If you aren’t sure about what cash flow in the second year is going to be approx., you probably shouldn’t even do the analysis. OF COURSE, you could have just as easily (and probably it’s more accurate) to say “Ya, I imagine 15% growth in second year is reasonable, but just to be safe, it could be between 13% and 15%”. Fine. So simply then discount back at 8% both numbers (which would be $2260-$2300)…now you have a range.
The point is though, there’s no point in messing with the discount rate. The turd in the bowl of cash flow is still a turd if you don’t get it right.
SO NOOOOW MARGIN OF SAFETY COMES IN.
Depending on whatever you want to use – 25%, 50%, 75%…if you had any confidence in your cash flow analysis whatsoever…if we use the $3971.87 cash flow 2 year figure, the MOS gives us the value of the cash flow as $2978.90, $1985.93, or $992.97 respectively.
But if we were that sure about our cash flow projection for year 2 above, we wouldn’t even need a large margin of safety…because margin of safety is to compensate for what we don’t know.
In any case, the last step is simply divide those respective MOS values by the shares – and buy if the price is at or below those figures respectively.
But I’d actually like to get your thought about this. Do you agree or disagree with what I typed above? Does it make sense or not? Ultimately, the argument is “but we end up at the same place at the end of the valuation”…but it seems that if one if discounting cash flow figures by 15% instead of the risk free rate – that individual probably doesn’t really know what they’re trying to do. Because if they did, they’d simply conservatively put thought into the cash flow figure each year, and the conservative growth of that figure…and then do the rest of the steps.
I imagine Buffett bought coca cola at 8.85% 10 year treasury in 1988 …and not 15%…for this specific reason. Because he knew what he was doing. He knew how to estimate the cash flows conservatively.
And no one says you have to buy if the figures don’t come out right. You simply wait until the price meets your conservative cash flow figures.
(P.S. The one thing I left out here is the value of everything BUT the cash flow, that you add to the cash flow figure…namely the shareholders value if the business was to liquidate today. This message is long enough already, but it would require probably recasting the current balance sheet [i.e. cash at 100%, Inventory maybe at 60% blah blah blah] – add that to the intrinsic value/cash flow figures – you got the Total Value of the Business today.)
Again, let me know if I’m not making sense.
August 28th, 2008 at 9:21 pm
Just realized for the analysis I put ($2300 / (1.08)^2)
That should have been ($2300 / (1.08)) WITHOUT the power 2. So, use your imagination for the calculations.
August 29th, 2008 at 12:07 pm
Hi J. Nice name
I’ll to keep it short and to the point so its easier to understand.
1. Discount Rates
What I didn’t go over very well in this post is the relevance of the discount rate to the investor.
What is a discount rate? It’s a rate of interest that would make an investor indifferent between present and future dollars.
The discount rate is very different to the cash flow return.
If you believe a 8% rate of interest for the future dollars is adequate, that is entirely up to you. I lean very strongly towards present dollars rather than future dollars. In other words, I use a high discount rate because I prefer the certainty of the present cash rather than the uncertainty of the future.
On the other hand, other investors may prefer to bet that the future will play out like they imagined, thus making future cash flows equally valuable to today’s cash flow.
Also, there is no single correct discount rate, and I don’t believe you can just use one discount rate for all companies. For simplicity sake of my posts, I just use 15%, but depending on the type of company, the discount rate should vary.
A company like Coca Cola will have a much stabler future cash flow than a tech company. Thus the future cash of Coca Cola can be considered to be just as good as today’s cash.
The tech company however, should you choose to perform a NPV, should emphasise today’s earnings rather than future earnings and should therefore require a higher discount rate.
2. Shareholders value and total business value.
I’m not quite sure what you meant in your comment, but I’ll take a stab at it.
Total business value depends on how you look at the business. E.g. inventory full of laptops wont be worth much when sold or liquidated, so defining the value of invetory at 100% of its value is quite flawed. If inventory was raw materials, it would be worth much more than computers sitting on shelves.
This also applies to machinery and other tangible assets. An old steel mill may be worth less than its stated value because others probably wont have use for its old and outdated technology.
Agree, disagree?
July 5th, 2009 at 6:07 pm
Hi Jae,
Great website – was going through some of the old articles trying to understand the spreadsheets better (we just purchased the premium version). Looks like the first image in this post isn’t linking correctly. Just heads up.
-Brian
July 5th, 2009 at 9:10 pm
Thanks for letting me know Brian.
Seems like I lost the file during my webhost transfer and I don’t have the original file anymore. Will have to remove the image.