Growth rates, the Rule of 72, and the danger of extrapolation

- Let's go way back in time to 1986. In early 1986, Walmart announced that sales for the year ended January 31, 1986 totaled 8.451 billion dollars. Now by the way, Walmart defines its accounting year as ending on January 31st rather than on December 31st. This is because, on December 31st, Walmart is still doing a substantial amount of holiday selling along with merchandise returns. December 31st is not a good time to slow things down to do the annual accounting. The closing of the books waits until a month later on January 31st. This is standard practice from many retail companies. Anyway, let's go back to that 8.451 billion dollar number. Does that represent good news or bad news? Well, I don't know about you, but I myself would be pretty pleased with an annual sales of over eight billion dollars. But we aren't talking about me, we're talking about Walmart. In order to say whether this is good news or bad news, we need a comparison, a bench mark. And the most natural benchmark is the amount of sales that Walmart reported in the prior year. The 1985 sales amount was 6.401 billion dollars. So sales were up in 1986 to 8.451 billion. But we can do even better analysis in this. Let's compute the percentage increase in sales from 1985 to 1986. The increase in sales is 2.050 billion dollars. That's 8.451 billion minus 6.401 billion. To find out the percentage increase, we divide the 2.050 by the beginning amount, the 6.401 billion in sales from 1985. Here's the computation. 8.451 minus 6.401, that's the change divided by the beginning amount, 6.401, that's 32.0%. Now that is a hefty sales increase. Most companies are happy with a sales increase of between 5% and 10%. So a 32% sales increase, that's fantastic. In fact, Walmart had similar sales increases in the following years. Here are Walmart's sales and sales growth rates for the years 1985 through 1995. Take a look at those. You'll see that in the earlier years, 1985 through 1989, Walmart's sales growth was averaging over 30% per year. In the later years, 1990 through 1995, sales growth has slowed down to closer to 25% per year. Still great, certainly. But just a little slower. Now, I'm going to teach you a trick. It's called the Rule of 72. The Rule of 72 tells you how long it takes an amount to double given a certain growth rate. You give me the growth rate, let's call it 24% just to keep things easy. The rule of 72 says that I divide 72 by the growth rate of 24% and that will give me approximately the number of years until the amount doubles. Let's try this with the Walmart sales data. Sales in 1992 are 43.887 billion dollars and sales are growing at about 24% per year for the following three years, 1993, '94 and '95. My prediction is that with 24% sales growth per year approximately, in three years, Walmart sales will approximately double. That's the 72 from the Rule of 72 divided by 24%, three years. So in 1995, you see that Walmart sales of 82.494 billion dollars are indeed approximately doubled the 1992 level of 43.887. Yeah, it isn't exact, but it gives a quick approximation. Remember this rule of 72, we'll use it again in a moment. Now, let's do something dangerous and a little foolish. Let's extrapolate Walmart's growth rate to predict what Walmart sales will be in say 2016. With sales growing at about 24% per year in 1995, then Walmart's sales should double every three years. To keep the arithmetic easy, let's say that Walmart's sales in 1995 are roughly 80 billion dollars. So three years later, 1998, sales should be doubled. Up to 160 billion. And again in 2001, they should double again to 320 billion. If we were to keep going in this process, we'd find that in 2016, after five more doublings, Walmart's sales would've reached 10.2 trillion dollars. That's amazing. This would represent $1,400 per year for every woman, man and child on the earth. Well, let's look at the actual numbers after 1995. Hmm, well, we see a couple things. First, sales in 2016 did not reach 10.2 trillion dollars. Second, we see that the reason is that Walmart's sales growth rate have slowed substantially. From 1996 to 2006, the annual sales growth rate is closer to 12% than at the 24% annual growth rate in the preceding 10 years. Remember in the Rule of 72, this means that Walmart went from doubling its sales from every three years, 72 divided by 24% to doubling its sales every six years. 72 divided by 12%. And then in the following years up until 2016, Walmart's sales growth rates slowed even further down to about 4% a year, implying a doubling time of 18 years. 72 divided by 4%. So instead of sales of 10.2 trillion dollars in 2016, as we estimated based on our extrapolation from the high growth years in the 1990s, Walmart's actual sales in 2016 were just 479 billion dollars. But what we see from the sales growth numbers is that Walmart is slowing down. Of course, there are several reasons for this. First, Walmart's early growth was in the United States. But now, there are Walmart stores everywhere in the United States. So continued growth has to be in international markets where Walmart is finding it more difficult to get a foothold. Also, once a company gets so big, it is hard to continue growing at such a high rate. For example, in 2015, Walmart's sales grew nine billion dollars. There aren't many companies that have nine billion dollars in total sales. But percentage wise, because Walmart is so big that nine billion dollar increase was just a 1.9% sales growth rate. Finally, online retailing has taken a toll on traditional brick and mortar stores such as Walmart. In fact, you see that in 2016, Walmart's sales actually decreased compared to the prior year. I wonder what will happen in 2017? So let's learn three things from Walmart. First, growth rates are a very good ways to understand the change in a business's sales in a country's population and a family's income. Second, the Rule of 72 gives a quick way to estimate the number of years it will take an amount to double. And third, there is a great danger in extrapolation. By blindfully extrapolating Walmart's sales and its growth rate based on 1995 data. We came up with a 2016 forecasted sales amount more than 20 times greater than the actual amount. What kind of similarly wrong conclusions can we make about what conditions will be like in 2037 by blindly extending 2016 growth rates. Extrapolate with caution.