Saturday, May 30, 2009

Working the numbers on the Toyota Prius

Okay, the Toyota Prius costs around $25K and gets around 45mpg in real-world driving on California freeways. The Toyota Yaris costs around $15K and gets around 35mpg in real-world driving on California freeways. So how many hundreds of thousands of miles at $4 per gallon would you have to drive the Prius in order to make that $10K worthwhile? What price would gasoline have to be to make a Prius more cost-effective than a Yaris over the typical 150,000 mile timespan that most people have a car?

First of all: let's look at the fundamental equation. C=G*M/E+P That is, total costs is number of miles divided by mpg, multiplied times the cost per gallon, plus the purchase cost.

So for the first question at 4mpg, we can model it as a 2x2 linear equation and for simplicity set the purchase cost at 10k for the Prius and 0 for the Yaris.

Prius: C1=4*M/45+10000
Yaris: C2=4*M/35
C1=C2 at: 4*m/45+10000=4*m/35... 10000=4*m/35-4*m/45... 2500=m/35-m/45... 2500=45m/1575-35m/1575 ... 2500=10m/1575 ... 3937500 = 10m ... 393750 = m.

So, working the math, at $4 per gallon you would have to drive the Prius for 393,750 miles over the course of its lifetime to make up the $10K cost difference over a Yaris.

So now let's find out what the cost of gas would need to be in order to make the Prius pay off at 150,000 miles:

Prius: C1=G*150000/45+10000
Yaris: C2=G*150000/35
C1=C2 at: G*150000/45+10000=G*150000/35 ... G*150000/35 - G*1500000/45 = 10000 ... 45 * G * 150000 / 1575 - 35 * G * 150000 / 1575 = 10000 ... 10 * G * 150000 / 1575 = 10000 ... 10 * 150000 * G = 15750000 ... G = $10.50.

In other words, gasoline would need to sell for $10.50 per gallon to make the Prius pay off over the Yaris over the typical 150K miles that most people keep a new car after buying it.

The Prius has some slight advantages over the Yaris. It's roomier, and much quieter inside under typical city driving conditions. On the other hand it also has some significant disadvantages. I'm fairly tall for a penguin, so I get a good view of the top of the windshield bezel if I have the seat fairly upright so I can see well around me (darn those beady little penguin eyes!). The performance is absolutely awful in mountains, once you exhaust the batteries while heading uphill you're basically limited to 45mph or slower. The handling is reminiscent of an old Volkswagen Beetle, in that the weight of all those batteries in the ass end make it want to trade places with the front end and the skinny tires have all the traction of black ice. All in all, once you get pass the gee-whiz factor, there just isn't any compelling reason for a single penguin (who doesn't care about the back seat kneeroom) to buy a Toyota Prius rather than one of the small 3 or 5 door hatchbacks now available for $10K less on the U.S. market. Assuming that the numbers on the cost sheet are similar to the amount of energy needed to create the vehicle, even the environmental argument doesn't work -- if it cost $10K more in energy to build the freepin' thingy at current energy prices, you'll be over 400,000 miles before you'll recapture that energy due to lower fuel use, and who the hell keeps a car for that long anyhow? It'll be at the crushers long before then... well, except the battery pack, which will be at a toxic waste dump (huh!).

-- Badtux the Numbers Penguin


  1. So now you sell your bike and buy a Japanese Windup Car ? A Phut Phut ??? Won't be much fun but it is cheap to comute in . Just don't wind up under a hummer's bumper .

  2. except every extra dollar you spend in gas -- a good chunk of it goes to the saudis.....and other fun countries

  3. But Dcap, it takes more energy to build a Prius than a Yaris. *much* more energy. Which is why the Prius costs so much more than the Yaris -- it takes a lot of energy to refine the copper and extrude it into those wires in the Prius's giant electric motor, it takes a lot of energy to build those nickel hydride batteries, and so on and so forth. So you can figure that the Prius took significantly more energy to begin with. If it was only $5K more energy, you'd still need to drive the Prius over 200,000 miles, or have gasoline at over $5 a gallon, to use less energy (i.e., send less money to the Saudis). It also takes more energy to send the Prius over here from Japan, since it's a larger car than a Yaris and thus you can fit fewer of them on a cargo ship.

    Does it really matter whether the Japanese send the Saudis dollars for the energy, or we do?

    w3ski: I live only 4 miles from work now that we've moved to the new offices, so buying a small Japanese car isn't in the cards, and if it was, it would probably be a Honda Fit, which definitely *is* fun -- thing drives almost as well as a Mini Cooper (i.e., like a go-cart), but is cheaper and roomier. This discussion was more prompted by a co-worker who asked whether it made sense for him to buy a Prius. Also we do not have many Hummers here in the SF Bay area. Well, except behind bedroom doors, but it is not my place to talk about the weird sex practices of monkeys, me being a penguin and all :-). It's not like when I lived in Texas and cars were the exception rather than the rule. Almost every car on the road here is a practical small Japanese or Korean car, or it's a BMW or Mercedes if driven by a successful executive. You see very few Hummers here, we already know we have big tools (we design the things, y'know?), so we don't need a Hummer to prove it.

    - Badtux the Energy Penguin

  4. I think the Prius is an experiment on which Toyota is trying to recoup their expenses. The technology is is in its infancy and possibly a stepping stone to a better mousetrap. Some nutcases have been able to get 1000 miles from a tank of gas on a Prius. To me, that indicates that there is potential for the technology to do better.

    To be honest though, until the technology matures more, I do not see the point other than the fad.

  5. Yeah, Toyota tries out new technologies on the Prius first, then transfers the ones that work to their other cars. Electric power steering is an example, it turned out to be more efficient, more compact, and require less maintenance than hydraulic power steering so it's getting used on other Toyota cars now.

    I know someone who is a total geek who has a Prius simply because of all the technology gadgetry. But let's face it, that's hardly a reason to buy a car unless you're a total geek...

    - Badtux the Technology Penguin

  6. Dude, if you're stuck in traffic the Prius isn't using ANY gas, the Yaris is.

  7. Well, I have a Prius - 2 years old - and I'm still getting 50-52 mpg overall. Granted, that still won't make the equation work. Nor will it help that gas is pretty cheap here. But, I love my little red car. When the gasoline engine cuts off and the silence begins, I think "Wow". I'm not much for the geeky things because I have to look at that blasted screen to change the fan speed, but I like the rear view camera.

    It's a better and cuter choice than driving the Highlander that I had...lots more fun, and I can still haul a full size recliner in the back with the seats down.


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