# Don't Buy a Prius to Save Money on Gas.

Originally posted on Oct 2012

You can now calculate different cars here:
DanNagle.com/2012/11/miles-per-gallon-break-even-point/

You know how it goes. You are at the pump. $50 in gas later, quite annoyed, your next statement is, “I should get a hybrid.” However, before you go buying, I would like to submit to you that a hybrid is not the way to go. Instead, you should just buy a cheaper car that uses less gas. Just like this title says, I will be using the Prius in my comparison. I have nothing particular against the Prius. I am just using it because it is the most popular hybrid. To compare, I will conveniently choose another Toyota car, the Yaris. This is to keep with a better apples-to-apples comparison. Sticking with the Toyota line helps factor in certain intangibles, like quality and general brand appeal. Both my cars will also be new. Lets begin. Car MSRP MPG-City MPG-Highway Prius$24,000 51 48
Yaris $14,111 30 38 I am going to give the Prius the best chance to win. Therefore, I am going to assume your Prius never leaves the city. My test will be 51 versus 30. That is a 21 mpg difference. Lets start with the expenses. First, you have to buy the cars. Car Item Prius Cost Yaris Cost Tally Prius Purchase$24,000 $0 -$24,000
Yaris Purchase $0$14,111 -$9,889 This is expected. A Prius is an “investment”. We make up the costs over time through gas savings, right? However, I submit to you that$10k is a pile of gas. Lets assume you live in a horrible gas market and paying $5/gallon. I am giving the Prius every chance to win this contest. How much gas do we break even? $\dfrac{\9,889}{\dfrac{\5}{\text{gallons}}} = 1,978 \text{ gallons}$ Our first “break-even point” is about 2,000 gallons of gas. That means we need to put 2,000 gallons of gas in to the Yaris to balance our spreadsheet. Lets do this. Car Item Prius Cost Yaris Cost Tally Prius Purchase$24,000 $0 -$24,000
Yaris Purchase $0$14,111 -$9,889 Yaris 1,978 gallons$0 $9,890$1

We have balanced the costs. Lets start driving! How far can we drive the Yaris before we run out of all that gas? I am using Yaris city MPG because Prius does significantly better in the city.

$1,978 \text{ gallons} * 30 \text{ MPG} = 59,340 \text{ miles}$

60,000 miles is a pretty good run before needing more gas. A salesman that is bad at math (or good depending on which side of the transaction you are on) might leave it at that by saying, “So after 60,000 with the Prius, or roughly a few years, it is all gas savings after that!” When he says that, you can respond, “No, sir. That covers only the initial up-front cost. I have to pay for that gas I used to drive that 60k.” The salesman will be shocked at your financial savviness and might even forgo his overpriced warranty pitch.

Anyway, so how much gas does it take to drive the Prius 60,000 miles? Once again, city driving because Prius is better at it.

$\dfrac{59,340 \text{ miles}}{51 \text{ MPG}} = 1,163 \text{ gallons}$

Lets add that 1,163 gallons to the Prius side of the ledger so it can catch up with the Yaris. Once again, we are using expensive $5/gal gas. Car Item Prius Cost Yaris Cost Tally Prius Purchase$24,000 $0 -$24,000
Yaris Purchase $0$14,111 -$9,889 Yaris 1,978 gallons$0 $9,890$1
Prius 1,163 gallons $5,815$0 -$5,815 OK, the Prius has just caught up with the Yaris. We are back to apples-to-apples comparison (2 cars driven the same distance). However, we had to buy ~$5,000 worth of gas to do it. We now need to give the Yaris that same ~$5,000 to balance our sheet. I’m adding some more columns to help our miles tracking. Car Item Prius Cost Yaris Cost Cost Tally Prius Miles Yaris Miles Miles Tally Prius Purchase$24,000 $0 -$24,000 0 0 0
Yaris Purchase $0$14,111 -$9,889 0 0 0 Yaris 1,978 gallons$0 $9,890$1 0 59,340 -59,340
Prius 1,163 gallons $5,815$0 -$5,815 59,340 0 0 Yaris 1,163 gallons$0 $5,815$0 0 34,890 -34,890

The Prius is behind again! What happened? Well, we need to take a step back. What you are seeing is the core reason that buying a Prius to save money on gas if fundamentally flawed and where so many get the math wrong.

You are only saving money on the difference between 51 MPG versus 30 MPG. Yes, the Prius gets good gas mileage, but so does the Yaris! The cheaper the gas and the closer the MPG, the more miniscule the savings. The Prius will catch up, yes, but you have to drive a pile a miles to do it. We already up to 94,000 miles and still haven’t hit break-even! Rather than keep going back-and-forth, I am going to start deriving formulas to quickly get the ultimate answer.

Cost to drive a Prius:

$\dfrac{51 \dfrac{\text{Miles}}{\text{Gal}} }{ \dfrac{\text{\5}}{\text{Gal}}} = 10.2 \dfrac{\text{Miles}}{\text{\}}$

Cost to drive a Yaris:

$\dfrac{30 \dfrac{\text{Miles}}{\text{Gal}} }{ \dfrac{\text{\5}}{\text{Gal}}} = 6 \dfrac{\text{Miles}}{\text{\}}$

I calculated that for every dollar, you can drive a Prius 10.2 miles or a Yaris 6 miles. I will use those numbers along with the up-front costs to derive a formula that finds the break-even miles.

$(\24,000 - \14,111) + \dfrac{X}{10.2 \dfrac{\text{Miles}}{\text{\}}} = \dfrac{X}{6 \dfrac{\text{Miles}}{\text{\}}}$
$X = 144,111 \text{ miles}$

144,111 is the break-even mileage. Now, I will find the number of gallons of gas each car needs as well as the the costs of the gallons. This will let me complete the table.

$\dfrac{144,111 \text{ Prius miles}}{10.2 \dfrac{\text{Miles}}{\text{\}}} = \14,128$

$\dfrac{144,111 \text{ Yaris miles}}{6 \dfrac{\text{Miles}}{\text{\}}} = \24,018$

$\dfrac{\14,128}{\dfrac{\5}{\text{Gal}}} = 4,803 \text{ gallons}$

$\dfrac{\24,018}{\dfrac{\5}{\text{Gal}}} = 2,825 \text{ gallons}$

Now, lets look at our final table.

Car Item Prius Cost Yaris Cost Cost Tally Prius Miles Yaris Miles Miles Tally
Prius Purchase $24,000$0 -$24,000 0 0 0 Yaris Purchase$0 $14,111 -$9,889 0 0 0
Prius 4,803 gallons $14,128$0 -$24,017 144,111 0 -144,111 Yaris 2,825 gallons 0$24,018 -$1 0 144,111 0 So there you have it. Assuming$5/gallon, and you drive your Prius only the city, you would have to drive 144,111 miles before you just break even over a Yaris!

This is an absurd number of miles just to save on gas, and gas prices could go down (note that I chose a high $5/gal). Also, I’ve made no assumptions of repairs. Your Prius will probably need a new battery before then, which can be$2,000 versus a $200 Yaris battery. Also, I made no assumptions for insurance. A Prius will cost more to insure than a Yaris. That is an increased monthly deflating gas savings the entire time it is owned. Also, no assumptions of financing. If you don’t have the full amount up-front, you are now financing an additional$10k. That could be another thousand in interest.

In short, saving money on gas is not a good reason to buy a Prius. The numbers don’t add up. If your motivation is environmental, I’d say the larger size, precious metals for complex parts, and alternate traveling options (public transit, motorcycles, or ride-shares) defeats that argument too.

If you just want to buy one because “it is cool”, I will not argue with that. It is a cool and fun car. Go ahead and buy it for that reason. Whatever the reason, know why you are buying it. Just don’t kid yourself that the reason is an “investment” to “save money” or “save the environment”.