Break Even Point for Fuel Efficiency Enhancements

Date July 1, 2009 by Isaac

On my way home from work yesterday I was pondering the question, "if I do modification foo to my car for a cost of bar dollars and it improves my fuel efficiency, then after how many miles is the break even point where that modification becomes cost effective?"  OK, I know that is a somewhat random question, but those are the types of questions my brain likes to solve.  So, I pulled out a pencil and some paper and after some thought derived the needed equation:

x = \frac{U_c E_1 E_2}{P (E_2 - E_1)}
Where:
x = Miles to break even
Uc = Upgrade cost in dollars
E1 = Fuel economy prior to upgrade (miles/gallon)
E2 = Fuel economy after upgrade (miles/gallon)
P = Price of fuel in dollars/gallon

So, for example, lets say that I put $75 into a modification to my car. Prior to the modification I got 18MPG and afterwards I get 20MPG. Let's also say that fuel costs an average of $2.99/gallon. The calculation would be:
x = \frac{75 \cdot 18 \cdot 20}{2.99 \cdot (20 - 18)}

Which works out to 4515 miles. So, if my car got 18MPG and I put $75 into a modification that brought the economy up to 20MPG it would take 4515 miles of driving to recover my costs. Anything after that would be saving me money.

There are a lot of scams out there for fuel saving devices. IF you can actually find something that works then you can use the above formula to calculate whether or not it would actually be worth the purchase.

Category Posted in Cars

One Response to “Break Even Point for Fuel Efficiency Enhancements”

  1. AvatarChris
    Posted: Jul 2nd, 2009 at 10:00 am
    1

    When gas was going up; myself driving a truck; a fairly significant number of my friends factored in buying a motorcycle to replace their suv to “save money on gas”. I worked out a spreadsheet that made all of them cringe on the point… (Erie; a bit worse weather wise that pgh; so numbers were worse there, I also factored in increasing gas prices). I am going to use your formula and modify it a bit to do the same…

    (bike cost) * (truck mpg) * (bike mpg)
    ————————————–
    (gas price) * (bike mpg*truck mpg)

    In [6]: (5000*15*40)/(2.99*(40-15))
    Out[6]: 40133.779264214048

    from kbb.com…
    (http://www.kbb.com/KBB/CompanyInfo/MotorcycleFAQ.aspx)
    8. What is the average yearly mileage for a motorcycle?
    Obviously mileage will vary from year to year and model to model. A simple guide could be to consider the type of bike you are looking at: If the bike is a sportbike 600 c.c. to 999 c.c., and since these bikes are traditionally weekend only bikes, you can expect to see lower miles, about 3,000 miles per year. Tourers or Sport Tourers usually see a lot of miles, but these are generally freeway miles, between 5,000 to 6,000 miles per year.

    This is nationally; due to weather; I will half that for Pittsburgh (shorter riding season + rain), and I’ll round up so 3500/year. So, that gives us…

    In [7]: ((5000*15*40)/(2.99*(40-15))/3500)
    Out[7]: 11.466794075489728

    If you buy a *cheap* used bike; put no money into repairs at all (or offset normal vehicle maintenance with the bike maintenance; in my experience, bike is a bit more prone to breaking down) it will take you ~11.5 years to break even on gas alone. Doesn’t factor in entertainment value or hospital bills either…:)

    -Chris

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