Problem of the Month

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Problem of the Month - April 2011

The price of gas keeps going up.  In California, most gas stations now charge over $4 even for the lowest octane gasoline.  Hybrid cars cost more, but are more energy efficient than most standard gasoline-only cars.  Hybrid cars are also better for the environment.  Are they better for your wallet as well?  Let’s figure out the break-even time for a hybrid car, and how much money you could save over the lifetime of a hybrid car.

Answer

This is a real-life question, one that a car buyer should think about.  Let’s start by making some assumptions.  Let’s assume:

  1. A standard new car would cost $20,000 and gets 24 miles per gallon. 
  2. The same or similar car with a hybrid engine will cost $27,000 and gets 40 miles per gallon.  In other words, a hybrid would cost $7,000 more.  
  3. On average, the car is driven 15,000 miles a year, and will last 10 years
  4. The price for gas is fixed at $4.00 per gallon

With these assumptions we can calculate how many years it takes to break even, given the price difference at purchase and the lower gas usage of a hybrid.  This also allows us to calculate what the savings are over the lifetime of the car.                                  

Step 1:  Figure out how much more gas a regular car uses than a hybrid in going 1 mile

The standard car gets 24 miles per gallon and the hybrid 40 miles per gallon.  A gallon of gas will allow a hybrid car to drive 40 miles, while a standard car will only travel 24 miles.  This also means that driving one mile will consume 1/40 of a gallon of gas for the hybrid, but 1/24 of a gallon for the standard car.  So for each mile, a standard car consumes 1/24 – 1/40 = (10-6)/240=1/60 gallons more gas.

Step 2:  Figure out the savings in one year

We assumed that a car is driven an average of 15,000 miles per year.  This means that the standard car will use more gas calculated by:

1/60 gallon per mile * 15,000 miles

= 1/60 * 15,000 gallons

= 250 gallons

At a cost of $4.00 per gallon, 250 gallons will cost $1,000.  So a standard car costs $1,000 more in gas per year than a hybrid car.

Step 3: Figure out the number of years it will breakeven

Since a hybrid saves $1,000 a year in gas, but costs $7,000 more to purchase, it will take 7 years to break even.

Step 4:  Figure out savings in the lifetime of a car

Assuming a 10 year lifetime, the first 7 years go to equalize the price of the hybrid and standard cars.  The remaining 3 years give the hybrid buyer some savings.  At $1000 saving per year, this yields a $3000 saving.  If the car lasts another 5 years for a total of 15 years, which is common in California, then the hybrid owner could save an additional $5000.

The above calculations assume the gas price stays at $4.00 per gallon; of course the savings are greater if the cost of gas goes up.  While the gas price in the U.S. has gone up substantially in the last several years, it is still much cheaper than in Europe, where high taxes are used to support other transportation systems such as rail.  Our calculation shows that a hybrid car definitely saves gas money in the long run.