## Tuesday, October 7, 2008

Dear Doctor Math,
Should I buy a Prius or a Honda Civic? At the Toyota dealership they told me the Prius pays for itself in gas savings, but I don't trust them.
Thanks,
Deke

Well, Deke, it's good to be skeptical. But let's see if we can crunch the numbers and settle this for ourselves without having to trust a car salesman to figure it out for us.

First, we'll have to make some assumptions about the costs of the various things in question and the ways that you're planning to use your car, whichever one you get. All of the numbers I'm about to quote came from the EPA's fuel economy website. Now, I don't know anything about you, but I'll go ahead and assume you drive about 15,000 miles per year, like the average American does. (Someday I'll write about the difference between "average" and "typical," but we'll table that discussion for now.) Of that 15,000 miles, I'll assume that approximately 55% is "city" driving and the other 45% is "highway," again in keeping with the average. So that works out to 8,250 miles in the city and 6,750 miles on the highway. If you're involved in a lot of cannonball runs, you can adjust accordingly.

According to the EPA's latest numbers, the 2009 Honda Civic gets 25 miles per gallon in the city, 36 highway. So, every year you would use 8,250/25, or 330, gallons of gas in city driving and 6,750/36, or 187.5, gallons on the highway. You total volume of gas used per year in the Civic would be 330 + 187.5, or 517.5 gallons.

Due to its greater efficiency in stop-and-go traffic, the Toyota Prius gets 48 miles per gallon in the city and 45 on the highway. Therefore, the total amount it guzzles per year is 8,250/48 + 6,750/46, or 321.8 gallons.

Now, gas prices are hard to predict, but let's guess that over the lifespan of your car, gas will cost an average of \$4.00 per gallon (in 2008 dollars). That seems like a reasonable projection given the way prices have historically risen. So that works out to 517.5*4, or \$2,070, per year for the Civic and 321.8*4, or \$1,287, for the Prius. Every year, that means you save \$783 by driving the Prius.

According to the manufacturers, the suggested retail price for the Civic is \$16,205; for the Prius it's \$22,000. These prices assume a basic package; probably, any extras you might want, like ground effects or those things that make it jump up and down, would cost about as much for either car. The difference in price, therefore, is \$5,795, which would take 5,795/783, or about 7.4, years to pay off in gas savings. Of course, if gas goes up even more, say to \$5 per gallon, that number would come down to as little as 6 years.

Either way, it seems like a fairly long time, but not outside the realm of possibility. I couldn't find any good numbers here, but people I know who own cars seem to get a new one about every 5 years. Maybe you hold to your cars a little longer, Deke, or maybe there might be other things about driving a Prius that appeal to you, I don't know. But strictly in terms of the gas savings, it doesn't seem to quite be worth it, although it's close. The market seems to have done a pretty good job sorting out these relative prices.

An interesting side-note here is that the marginal gas savings (that is, the money saved per every additional mpg) go down as the cars get more efficient. For example, doing the same calculation as before, we can see that an SUV that gets 10 miles per gallon costs \$1,000 more per year in gas than one that gets 12 miles per gallon. So, the more important choices may not be between pretty good and very good, but between bad and very-slightly-less-bad.

-DrM

Melissa said...

Hey Deke. I'm also wondering how much you value your time and what climate you live in. Personally, I found filling my gas tank every week to be annoying and time-consuming (and cold during the winter months). If you figure on 20 minutes for the entire ordeal including extra travel and gas pumping, that's more than 17 hours every year. So if you're interested in halving that figure, then you might be inclined toward the Prius. Or even better, if you can associate a dollar amount with the value of your time, then you can do the calculation yourself!

drmath said...

Of course, you're assuming that the Prius and the Civic have the same size gas tank. In fact, the Civic has a capacity of 13.2 gallons, and the Prius uses a flexible bladder system (to eliminate fuel vapors), which at its maximum is 12 gallons but contracts in the winter to about 6 gallons. I believe the industry standard is to aim for 400 miles per tank, so the number of refills should be the same on average.
-DrM

Zachary said...

Doctor Math, your final point on diminishing marginal gas savings was covered well (albeit from an emissions standpoint) in this NPR piece from several months back.

DU said...

As a math nerd myself, I love the blog but I feel compelled to comment on this entry: An over-emphasis on the pure mathematics of payback times is exactly how we got into this climate change problem. We should switch from Civis to Priii not because it's cheaper in gas but because it is better in ways not captured in the financial numbers.

(Actually, you probably could tease out some of the financials by looking at how much we'll have to spend to clean up after ourselves. Basically, assigning a cost to pollution. But I hesitate to use a method that once again puts money in charge of policy, rather than human beings.)

drmath said...

An excellent point, DU, and one that I should have made more clear. The original question was whether the Prius "pays for itself" in gas savings, which is a straightforward calculation. But as you rightly say, there can be many other considerations that would affect whether you actually bought the car, many of which can't be reduced to a single number. And I absolutely agree that the short-term savings approach to decision-making is a huge problem, environmentally. (Side note: for what it's worth, I actually talked my parents into buying a Prius using this same argument.)

Thanks for the reminder.