# Matt Franz : Zealous For Knowledge

## Fermi Estimation For Investors

Buffett and Munger famously council not to buy anything you don’t understand and can’t value in your head or on the back of an envelop. One of the best mental models for this type of investing is Fermi Estimation.

Enrico Fermi famously estimated the energy released at one of the early atomic bomb tests just by watching how far the blast blew a few scraps of paper.

The goal of Fermi estimation is not to get a precise answer – it’s to get an answer that’s the right order of magnitude. From there, the estimate can be refined as necessary.

This works for investors because we want to buy something that screams out at us – something that is worth an order of magnitude more than it’s price. If you can’t see that with rounded numbers on the back of the envelop, there’s probably not a large enough margin of safety present.

Fermi Estimation has five steps:

1. List the assumptions and key factors.
2. Estimate the value of each factor. If you are unsure, chose an obvious lower bound and upper bound and take their geometric mean (square root of the product of the lower and upper bound).
3. Combine your factors as needed to get an order-of-magnitude estimate. Round and use scientific notation to make the math easy enough to do in your head.
4. Interpret your results and convert it to a known quantity. You many want to convert the units to something more graspable or useful.
5. Refine each step. Question your assumptions. Repeat.

As an example, I am going to take a stab at valuing Tesla. I’ve never read Tesla’s annual report so I don’t have any specific knowledge of it. But I’ve read about the company in the papers and have studied other car companies.

Assumptions:

• Tesla only sells cars in the U.S.

Key Factors:

• Number of people in the U.S. – 300 million (3*10^8)
• Percent of people in the U.S. that buy a Tesla
• Lower bound = 1%
• Upper bound = 100%
• Geometric mean = 10% (10^-1)
• Tesla’s sold in a year (i.e how often do people buy a car)
• Lower bound = 1 year
• Upper bound = 10 years
• Geometric mean = ~3 (3*10^0)
• Profit per car sold
• Lower bound = \$100 (10^2)
• Upper bound = \$10,000 (10^4)
• Geometric mean \$1,000 (10^3)
• Market multiple on Tesla’s net income
• Lower bound = 5
• Upper bound = 20
• Geometric mean = 10 (10^1)

total buyers = 3*10^8 x 10^-1 = 3*10^7

total profit = 10^3 x 3*10^7 = 3*10^10

profit per year = 3*10^10 / 3 = 10^10

market value = 10 x 10^10 = 10^11

Tesla could have a market cap of 10^11. This is \$100 billion dollars. Currently Tesla’s market cap is \$58 billion dollars and Ford and GM’s are, respectively, \$42 and \$60 billion.

I got all of this without any data – I just guessed. Now I want to question my assumptions and make a more educated guess. My first suspect is profit per car. I assume Tesla makes \$1,000 per car, but the data shows that Ford, GM, and Toyota all make well below that. On the other hand Porsche makes \$23,000 per car and Audi makes \$5,000. Those brands might be a better estimate for Tesla.  If I use a lower bound of \$500 and upper bound of \$23,000 the new geometric mean is about \$3,000.

Right now Tesla loses \$4,000 on every car. So the potential estimates are all over the place. If Tesla someday earns \$3,000 per car my estimate would be 3x higher (\$300 billion, 5x its current price). If it earns what GM and Ford make per car, it would be 50% lower. If Tesla never earns a profit it’s value is below zero.

This is clearly a decisive factor. I’m willing to stop my analysis here because Tesla’s current state is so far from a state where my estimate makes sense. Investing in Tesla today is a bet that it begins to turn a profit on each car. I’m going guess that there’s a 30% chance Tesla achieves a \$1,000/car margin and 70% chance it never turns a profit. Reasonable people could disagree on this.

My expected value for Tesla is therefore: 0.3 * 100 billion + 0.7 * 0 = 30 billion. This is about 1/2 of Tesla’s current market cap, so the market has a rosier outlook for the company than I do.

When I invest I look for the no-brainers. These are investments that show an order-of-magnitude mis-valuation using very realistic and conservative assumptions. Since Tesla doesn’t make money now, buying it is a bet on Elon Musk. I certainly wouldn’t bet against him, but he isn’t a variable I’m willing to hang my hat on.

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