## Problem of the Month - February 2011Last month we talked about compound interest. This month we will use the compound interest concept and do a real-world problem, a kind of exercise often performed by financial analysts. Netflix is a company that provides movies for viewing, either by streaming online or by mailing a DVD to your home. As a company, it has done extremely well. Its revenue (the total amount of money it receives from all of its customers) was $1.21B (billion) in 2007, $1.36B in 2008, and $1.67B in 2009. Here is the problem: What was Netflix’s average revenue growth rate from 2007 to 2009? If it continues to grow at that rate, how big will the revenue be in 2015? ## AnswerThis kind of analysis is done all the time by financial analysts. You can see from this how elementary school math is used in real life. This is a percentage problem. In 2007, the revenue was $1.21B, and in 2008 the revenue was $1.36B. So the revenue increased by $1.36B – $1.21B = $0.15 B. To convert this to a percentage, we need to divide the increase by the original amount, and multiply by 100: 100 x 0.15/1.21 = 12%. Hence the revenue increased by 12% from 2007 ($1.21B) to 2008 ($1.36B). To do this, we just need to repeat the same steps as above. Alternatively we can look at the ratio of the 2009 revenue to the 2008 revenue: 1.67/1.36 = 1.23. To get the percentage growth you need to subtract 1 from this, and then multiply by 100. This means the growth rate was 23%. This is a quicker way to figure out the growth rate, using a different formula that of course gives the same answer (you can check that this is the case). The growth rate from 2007 to 2008 was 12%, and that from 2008 to 2009 was 23%. The average of 12% and 23% is 17.5% (add 12% to 23% and divide by two). So the average growth rate between 2007 and 2009 was about 18% (I rounded it up to make it easier. Also, I did not use the compound growth rate but an average growth rate). If the growth rate is 18% every year, then the revenue in future years is obtained by multiplying the revenue by 1 plus 0.18 (18% divided by 100):
So if Netflix can continue on its current growth trajectory, it will almost triple its revenue by 2015, to $4.5B! Of course, it is not easy to continue to grow at such a high rate. But Netflix still has a lot of room for growth: It has 20 million members at present. In the U.S., we have 150 million households. So they only have 7.5% of the households in the U.S. as customers (100 times 20 million divided by 150 million), which an analyst would say means their market share is under 10%. I can see that this company could likely obtain maybe 30% of the U.S. households as customers. Of course there is also the potential for growth in the international markets as well. |

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