Compound Annual Growth Rate Formula
I've been away for a month and during that time the skyrocketing price of gas has received a lot of press. Having worked in the oil industry summers while in school, I've always found it interesting how people react to the price of gas. Until recently my thought had been that the price of gas had not kept up with inflation and the we in the U.S. should be probably be paying four to five dollars per gallon. However, I've never thought to prove my theory out until now.
In an effort to track what the price of gas has done over time, I first visited the U.S. Department of Labor's Consumer Price Index page. The first area of information I wanted to find was the Consumer Price Index for All Urban Consumers. Using January 1984 as the base, I set the base CPI for my analysis at 101.90. I then copied each monthly value from January 1984 to April 2008 into an Excel spreadsheet. Next, I retreived the average price per gallon values for regular unleaded gasoline for the same time period. To get an inflation adjusted price for gasoline, I multiplied the base price of gas (January 1984) by the CPI for the month. The results appear in the chart below. The year is on the X axis and the price per gallon of regular unleaded is on the Y axis.
The chart shows that the price per gallon of regular unleaded remained essentially flat from 1984 to 2000. After a small bubble that occurred from 2000 to 2002, the price starts to increase at a pace of over 20% per year. The 20% figure is calculated using the Compound Annual Growth Rate formula. The formula is:
( Future Value / Present Value ) ^ ( 1 / Number of Periods ) - 1
Excel's XIRR function can also be used to perform this calculation. The Analysis Toolpak must be installed for this function to work.
In January of 2002, the price of regular unleaded averaged $1.14. Five years later the price averaged $3.05. Using the formula above to calculate the compounded annual growth rate . . .
( $3.05 / $1.14 ) ^ ( 1 / 5 ) - 1 = 21.75%
Using 1984 as the base, the chart shows that the average price of unleaded gas exceeds the inflation adjusted price somewhere around 2006 to 2007. Unfortunately all of the growth has taken place in the last five years and it really doesn't start to stand out until 2004 - 2005. Based on inflation, it looks like my $4 to $5 price target may have been too high. Or, maybe $4 to $5 is the reality and the CPI is not reflecting that growth yet because the overall economy hasn't fully priced in current gas costs.
On another note, in the summer of 2004 I parked my truck and started to ride my motorcycle everywhere. I like to tell people that I anticipated the rising price of gas but the truth is that I just wanted to start riding a motorcycle instead of driving a car. Co-workers like to tell me "oh, you must be saving a lot of money by riding a motorcycle to work every day instead of driving a car". Although the bike does get between 40 to 50 mpg depending on driving conditions, I'm not sure that I'm really saving any money. What they don't realize is that I purchased a new motorcycle as opposed to driving a truck that was paid for. I recently figured I would have to ride the motorcycle for about ten years if I thought I was going to break even based on gas prices. I may be saving gas but I'm not saving any money, at this point anyway.
