### Author Topic: Help me with some math  (Read 5863 times)

#### Rust

• Posts: 87
##### Help me with some math
« on: October 16, 2013, 06:38:24 AM »
I'm trying to figure out what the break even point would be to buy a different car which has better gas mileage.

I currently drive a 2006 Nissan Altima.  135k miles on it.  I average 26 MPG.  (I chart my fill ups so I'm pretty confident about this number)

I drive about 8,400 miles per year @ 26MPG that's 323 gallons of gas/year
Goal MPG for a different car would be 35 MPG.  that's 240 gallons of gas/year

For a difference of 83 Gallons/year.  Gas has averaged about \$3.30 for the past year in my area.  Let's just assume this is a constant for now.  Savings for different car would be ~\$275 per year.

If I sell my current car for \$5,000 how much more should I be willing to pay above that \$5,000 for a replacement.  Also assuming replacement should have a longer assumed service life.  I figure I've got about another 6-7 years with the Altima.  ~200k miles.

Or the alternative hypo., Keep the Altima, drive it until it catches on fire/melts/explodes/leaves me stranded in the middle of nowhere but I end up with an awesome story about how some random person saved me.

#### exranger06

• Stubble
• Posts: 100
• Age: 33
• Location: CT
##### Re: Help me with some math
« Reply #1 on: October 16, 2013, 07:51:08 AM »
If you keep the Altima until it's dead, what will you do then to replace it? Buy a brand new car? Buy a used car worth about \$15k? Used car worth \$3k? I think that's a key piece of information that's needed to answer your question.

I think you should compare the scenario of keeping the Altima until it's dead and replacing it with ___"X"___ and the scenario of skipping ahead and selling the Altima now and replacing it with ____"X"_____.

#### Rust

• Posts: 87
##### Re: Help me with some math
« Reply #2 on: October 16, 2013, 08:38:31 AM »
How much I'm willing to spend to replace is ultimately what I'm trying to solve for.  But, I don't want to start with I'll spend up to \$10,000 for a replacement. (which is actually the most I'd ever consider spending.  Really seems crazy high)

Thinking this through more.  based on improvements to MPG, there should be a savings attached to each MPG.

So if 35 MPG = \$275 per year which is a 9 MPG improvement each MPG above 26 is worth \$30.55.

MPG/improvement in MPG/Savings for a year/Savings over 6 years
I'm assuming residual value after 6 years to be \$0.
26/0/\$0/\$0
35/9/\$275/\$1,650
40/14/\$428/\$2,568
45/19/\$580.45/\$3,482.70

Here's my conclusion, someone let me know if it makes sense.

I should be willing to pay \$6,650 for a car that today gets 35/MPG, \$7,568 for a car that gets 40 MPG.*

*each price I'd be willing to pay would also need to factor in annual car tax and insurance differences which may or may not exist on a purchase by purchase basis.  For simplistic purposes, I'm leaving that out of this calculation but trust me it would be part of the consideration given.

#### ritchie70

• Bristles
• Posts: 268
##### Re: Help me with some math
« Reply #3 on: October 16, 2013, 08:49:23 AM »
Your described methodology seems reasonable to me but I didn't check the numbers. Make sure you compare apples to apples on fuel economy though.

For example (made up numbers) if you get 26 MPG, but EPA says combined is 30 MPG, then you're managing to get 14% under EPA estimates. Since you can't borrow the car for a month and calculate what MPG you're going to get, I guess you should just assume that you'll do 14% under the other car's EPA combined economy too.

Be warned that EPA calculation methodology changes over time, so make sure you're comparing numbers derived in the same way.

#### okashira

• Bristles
• Posts: 416
##### Re: Help me with some math
« Reply #4 on: October 16, 2013, 09:38:13 AM »
How much I'm willing to spend to replace is ultimately what I'm trying to solve for.  But, I don't want to start with I'll spend up to \$10,000 for a replacement. (which is actually the most I'd ever consider spending.  Really seems crazy high)

Thinking this through more.  based on improvements to MPG, there should be a savings attached to each MPG.

So if 35 MPG = \$275 per year which is a 9 MPG improvement each MPG above 26 is worth \$30.55.

MPG/improvement in MPG/Savings for a year/Savings over 6 years
I'm assuming residual value after 6 years to be \$0.
26/0/\$0/\$0
35/9/\$275/\$1,650
40/14/\$428/\$2,568
45/19/\$580.45/\$3,482.70

Here's my conclusion, someone let me know if it makes sense.

I should be willing to pay \$6,650 for a car that today gets 35/MPG, \$7,568 for a car that gets 40 MPG.*

*each price I'd be willing to pay would also need to factor in annual car tax and insurance differences which may or may not exist on a purchase by purchase basis.  For simplistic purposes, I'm leaving that out of this calculation but trust me it would be part of the consideration given.

How Much Can I Afford? and How Much Can I Justify calculations, even if done with good intentions, will always lead to inferior results.

The right answer is to find the cheapest car that will be safe, reliable and fulfill your needs.

You can buy that 35mpg car for \$4000, so do it.

#### grmagne

• Posts: 65
• Location: Toronto
##### Re: Help me with some math
« Reply #5 on: October 16, 2013, 09:44:06 AM »
This post is a nice tie-in to http://www.mrmoneymustache.com/2013/10/15/when-energy-saving-becomes-an-emergency/

I'd recommend getting into the habit of using interest in your calculations as well, to get the true MMM seal of approval.  For example, if you assume that you can get a 2% rate of return on an investment, then buying a more expensive car saves money but costs you on potentital investment money.  In this case, you could type 2% into cell A1 in Excel, 6 (years) into B1 and \$275 (annual gas saving) into C1.  Then in D1, type the formula =C1*(1-(1+A1)^-B1)/A1

This should produce the result \$1540.39, which means you should pay no more than \$6540 with a 2% interest assumption.  At 6% the limit would be \$6352 because you're less willing to buy an expensive car if you're getting a great rate of return on your existing capital.

To test other scenarios, you can copy all the cells A:D down in new rows and then build a table of various interest rate and MPG scenarios.

BTW, technically you should use a monthly rather than an annual compound interest formula, but for simplicity it's easier to illustrate the annual formula -- the results aren't that much different in this case anyway.  And inflation is implicitly stripped out of all the gas & interest calculations, so just use the after-inflation rate of return.

#### Rust

• Posts: 87
##### Re: Help me with some math
« Reply #6 on: October 16, 2013, 10:05:37 AM »
How much I'm willing to spend to replace is ultimately what I'm trying to solve for.  But, I don't want to start with I'll spend up to \$10,000 for a replacement. (which is actually the most I'd ever consider spending.  Really seems crazy high)

Thinking this through more.  based on improvements to MPG, there should be a savings attached to each MPG.

So if 35 MPG = \$275 per year which is a 9 MPG improvement each MPG above 26 is worth \$30.55.

MPG/improvement in MPG/Savings for a year/Savings over 6 years
I'm assuming residual value after 6 years to be \$0.
26/0/\$0/\$0
35/9/\$275/\$1,650
40/14/\$428/\$2,568
45/19/\$580.45/\$3,482.70

Here's my conclusion, someone let me know if it makes sense.

I should be willing to pay \$6,650 for a car that today gets 35/MPG, \$7,568 for a car that gets 40 MPG.*

*each price I'd be willing to pay would also need to factor in annual car tax and insurance differences which may or may not exist on a purchase by purchase basis.  For simplistic purposes, I'm leaving that out of this calculation but trust me it would be part of the consideration given.

How Much Can I Afford? and How Much Can I Justify calculations, even if done with good intentions, will always lead to inferior results.

The right answer is to find the cheapest car that will be safe, reliable and fulfill your needs.

You can buy that 35mpg car for \$4000, so do it.

Agree with this statement whole heartily.  If I can find that 35 mpg car which would have a comparable expected life (6 years) for less than the current value of the Altima then it's a done deal, no brainer.

It's the flip side of the equation I wanted some help with on my math.  How much more should I be willing to spend above the value of the car right now.  grmagne did a very nice job showing me how I should include assumed rate of return into the calculation.  Thank you.
« Last Edit: October 16, 2013, 10:08:57 AM by Rust »

#### Ottawa

• Handlebar Stache
• Posts: 1033
##### Re: Help me with some math
« Reply #7 on: October 16, 2013, 10:07:25 AM »
Getting under the EPA means that you may have some room to improve your current car's economy through driving habits!

Having a look here: http://www.fuelly.com/car/nissan/altima/2006 gives a good idea of real world numbers.  You may be able to get to 28mpg with driving habit...but that's not getting you much closer to 35mpg.  I would use fuelly.com when considering other cars (to calculate real world economy).

I think Okashira makes a pretty good point.  That is - why do you have to spend more?!  You can easily get a car for 5K or less that achieves 35MPG and more.

Try a honda civic: http://www.fuelly.com/car/honda/civic

or toyota yaris: http://www.fuelly.com/car/toyota/yaris

Here is an example in the Ottawa area of 45 vehicles that are year 2000 and greaert, toyota yaris/echo, civic...manual transmission (of course) and 3500-5000 bucks and under 100,000 miles on the clock!

http://ottawa.kijiji.ca/f-cars-vehicles-cars-trucks-W0QQAQ5fCarBodyTypeZconvQ2ccoupQ2chtchbckQ2cothrbdytypQ2csedanQ2cwagonQQAQ5fCarMakeZhondaQ2ctoyotaQQAQ5fCarMileageInKmsQ5fmaxZ180000QQAQ5fCarModelZcivicQ2cechoQ2cyarisQQAQ5fCarTransmissionZ1QQAQ5fCarYearQ5fminZ2000QQCatIdZ174QQmaxPriceZ5Q2c000QQmaxPriceBackendZ500000QQminPriceZ3Q2c500QQminPriceBackendZ350000

#### grmagne

• Posts: 65
• Location: Toronto
##### Re: Help me with some math
« Reply #8 on: October 16, 2013, 10:12:47 AM »
BTW, technically you should use a monthly rather than an annual compound interest formula, but for simplicity it's easier to illustrate the annual formula -- the results aren't that much different in this case anyway.  And inflation is implicitly stripped out of all the gas & interest calculations, so just use the after-inflation rate of return.

I'm not able to modify my original post anymore for some reason, but here are the built-in Excel function for Present Value:

Annual
=PV(A1,B1,C1)

Monthly
=PV(A1/12,B1*12,C1/12)

#### Rust

• Posts: 87
##### Re: Help me with some math
« Reply #9 on: October 16, 2013, 10:17:24 AM »
To be clear.

I understand how this came across reading the replies.  I'm not saying that I'm going to spend more or even want to spend more.  I wanted to figure out how much more Should  be willing to spend based on what I currently own.

#### Rust

• Posts: 87
##### Re: Help me with some math
« Reply #10 on: October 16, 2013, 10:37:15 AM »
did a quick search on cars.com.

Only 1 Yaris under \$5,000 for sale within 250 miles of Richmond, VA.  125K miles selling for \$5,000.

I found a number of civic's all priced around \$5,000 with an average of 100,000 miles on them.

The conclusion I draw from these two quick searches is the used car market for fuel efficient cars is either lacking in supply or the demand has driven the prices up compared to other markets.

*Edit.  Did a search within 100 miles for all of the recommend by MMM on the Top 10 for Smart (http://www.mrmoneymustache.com/2012/03/19/top-10-cars-for-smart-people/)

Only seven came in under \$5,000.  This is what the only one under 100K miles looks like.

« Last Edit: October 16, 2013, 10:50:11 AM by Rust »

#### NumberCruncher

• Pencil Stache
• Posts: 612
##### Re: Help me with some math
« Reply #11 on: October 16, 2013, 10:58:42 AM »
http://www.consumerreports.org/cro/2012/12/what-that-car-really-costs-to-own/index.htm    love the graphs here and the data they looked at -- seems to be applicable to the OP's question.

#### Ottawa

• Handlebar Stache
• Posts: 1033
##### Re: Help me with some math
« Reply #12 on: October 16, 2013, 11:28:13 AM »