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Problem of the Month - February 2011

Last 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?

Answer

This 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.

Step 1: Let’s figure out the growth rate from 2007 to 2008.

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).

Step 2: Let’s figure out the growth rate from 2008 to 2009.

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).

Step 3: Let’s figure out the average growth rate.

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).

Step 4: Let’s forecast the revenue in 2015 assuming an annual growth rate of 18%.

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):

In 2010, revenue_2010 = $1.67B x (1+0.18)
= $1.67B x 1.18
= $1.97 B
In 2011, revenue_2011 = revenue_2010 x (1+0.18)
= $1.67B x (1+0.18) x (1+0.18)
= $1.67B x (1+0.18)^2
= $1.67B x 1.18^2 (I am not going to compute this, instead I want to get the expression right, and then compute once at the end)
In 2012, revenue_2012 = $1.67B x 1.18^3
In 2013, revenue_2013 = $1.67B x 1.18^4
In 2014, revenue_2014 = $1.67B x 1.18^5
In 2015, revenue_2015 = $1.67B x 1.18^6
= $1.67B x 2.70
= $4.51B

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.