Rule of 72

While reading the book 'The Intelligent Asset Allocator' by Dr. William Bernstein, I came across a useful rule of thumb related to compounding. As per the rule, the number 72 divided by the annual compounding rate gives the approximate number of years it takes for an investment to double. e.g. 72 divided by annual compounding rate of 9% equates to 8 years. The equation can also be used to estimate the annual compounding rate required to double the money in a certain timeframe. e.g. 72 divided by 6 years equates to 12% annual compounding rate.

The Rule of 72 can also be used to compare the relative multiple of a stock to another stock or to the market. e.g. suppose a hot stock like Asian Paints India Ltd which already has about 70% market share in the paint industry is trading at twice the P/E multiple of the paint industry in general. In order to justify the valuation solely on the basis of P/E, its earnings would have to grow at 5% rate relative to the industry for the next 14 years! Offcourse the valuation of a company hinges on many other factors and Asian Paints has exhibited higher profitability & growth which may justify its higher P/E but the Rule of 72 provides a quick & easy way to compare valuations in terms of growth rates. Disclaimer: I own Kansai Nerolac Paints and that is probably the reason I despise the higher valuations commanded by Asian Paints.

As per the Wikipedia entry on Rule of 72, one can use the numerator 69 or 70 for more accurate results when dealing with shorter compounding periods like continuous/daily compounding.