One of the most important mental models advocated by Charlie Munger (Trades, Portfolio) is mathematics. Munger’s partner, Warren Buffett (Trades, Portfolio), is a math prodigy. The ability to use mathematics as a tool to figure out the investment implications is one of Buffett’s widest moats. It takes me a while to get the importance of figuring out the basic math for many of the concepts we talk about in investing. Even professional investors often fail to perform the mathematical computations that are essential. Consider the following half real-world, half made-up questions.
1. A business can grow its sales 3.8% a year. Cost of goods sold increases 2.3% a year and total operating expenses increase 3.1% a year. The tax rate will decrease from 37.7% to 31.7%. The company will shrink its share count 1% every year. Assuming all of these will go on for 20 years, how fast can gross profit, operating profit, net income and earnings per share grow for the next 20 years?
Let’s say there’s another business that can grow its sales 5% a year. But cost of goods sold, operating expenses and taxes also grow at 5% a year. And the company doesn’t buy back any shares. Assume this company can also maintain this momentum for 20 years.
Question: Which company is a better choice if both companies are trading at the same P/E multiple and both have a current dividend yield of 2%?
2. A company can earn 12% return on equity and currently trade at 2 times book value. In the next five years, the company has the capability to reinvest all its earnings back in the core business or make acquisitions that will generate similar returns. However, at the end of the five-year period, the company can only reinvest half of its earnings, meaning the other half of the earnings will either be retained or distributed as dividend.
Question: What is your estimated return from the investment for the next five years and should you invest in this company if your opportunity cost is 10%? What if the company can reinvest two-thirds of its earnings in five years instead of only half? How would that change your expectation?
3. Another business is facing the following two options when it comes to an additional round of financing of $100 million with an expected pay-off date of June 2020:
Option 1 – borrow from the banks a year.
Option 2 – offer a 3% $100 million convertible senior notes with interests payable semi-annually. The conversion rate is 46 shares per $1,000 notes. In connection with the notes, the company enters into a capped call transaction to reduce potential dilution of the common stock. The cap price is $26 per share. Let’s say the company has to pay $10 million for banker fees and if the capped call option gets settled, it has to pay another $15 million settlement fee.
Question: At what interest rate would you choose to borrow from the bank instead of issuing this complicated convertible notes? 7%? 9%? 10%?
What you may have found out is that the three questions above each represents a different level of math. Question 1 is about operating leverage, and I have provided the answer in another article I wrote (link here). The first company in question is Brown Forman (BF.B, Financial). To some extent this is how Nestle (NSRGY) operates as well.
Question 2 is about the implications of capacity to reinvest, a concept that I talked about in my recent article about Tom Russo (Trades, Portfolio). This question is much harder than Question 1 because it requires a deeper understanding of investment concepts but the good news is, if you take the time and figure out the solution, you will immediately see the importance of capacity to reinvest.
Question 3 is a real-life example of how a company chooses to finance. Warren Buffett (Trades, Portfolio) would have figured this out in less than a minute, and it took me a humiliating amount of time to figure out. The math is a bit complicated, and you need to have an understanding of capped call transaction and convertible bonds in order to carry out the calculation.
I am not writing this article to argue that we should all go out and find fun math problems such as Question 3 above. I think being able to figure out Question 1 and Question 2 above should be sufficient. Every moat will be reflected in the numbers over time. In Brown Forman (BF.B, Financial)’s example, you can see how pricing power and advantage of scale translate into increasing margins and faster earnings growth. The end goal for us should be to tie the math to the qualitative factors; in other words, put a layer of numeracy on top of the literacy layer.
