Saturday, August 08, 2009

The Law Of Diminishing Returns, or Cash for Clunkers for Dummies

Years ago, when I drove a Honda Civic that got 40 miles to the gallon, I dreamed of a car that did better. In fact, I once had a car that got 23 mpg and I never forgave it. This was because my very first car was a diesel VW Rabbit which got 55 mpg no matter how badly I drove. (Ok, I used to like to park the jerks who thought they were going to use a left-turn-only lane to pass me at stoplights. Did I mention I went through my first clutch pretty quickly? That was definitely not cost-effective.)

So one day I whined to an engineer friend that I missed my Rabbit because my Civic wasn't as good on gas. He tried to explain to me the law of diminishing returns, and I couldn't buy it.

So when the Honda Insight came out, I built myself some spreadsheets to see how long it would take me to save the price of the car. I was horrified to discover that I never would. Not unless I could get 80mpg or the price of gas went up to $4/gal. and stayed there for the life of the car.

I bought the car anyhow and I've never been sorry. In fact, I now own one Insight (lifetime mpg 61.3 and fast approaching 200,000 miles) and one Hybrid Civic (no lifetime average - usually does better than 50 mpg on a tank and just past 50,000 miles).

If the law of diminishing returns doesn't mean anything to you, consider the following spreadsheet.


Cost to drive 10,000 miles


dollars per gallon


1 2 3 4 5
miles per gallon 10 $1,000 $2,000 $3,000 $4,000 $5,000
15 $667 $1,333 $2,000 $2,667 $3,333
20 $500 $1,000 $1,500 $2,000 $2,500
25 $400 $800 $1,200 $1,600 $2,000
30 $333 $667 $1,000 $1,333 $1,667
35 $286 $571 $857 $1,143 $1,429
40 $250 $500 $750 $1,000 $1,250
45 $222 $444 $667 $889 $1,111
50 $200 $400 $600 $800 $1,000
55 $182 $364 $545 $727 $909
60 $167 $333 $500 $667 $833
65 $154 $308 $462 $615 $769


So, at $1/gal, my old Civic cost me $250 to drive 10,000 miles. My Insight would cost me $167 to drive the same distance. I would say over the life of the car, gas has averaged a little over $2/gal. So, old car math - $2/gal price of 10,000 miles = $500 * 20 = $10,000 spent in gas over 200,000 miles. Insight math - $2/gal price of 10,000 miles = $333 * 20 = $6,660 spent in gas over 200,000 miles. So over the past 200,000 miles I've saved $3,340.

Now, let's just say you decided to participate in the cash for clunkers program. Let's say you turn in a car that gets you 15 mpg for a car that gets you 20 mpg. Let's say you drive this car for no more than 50,000 miles. Old car math - $2/gal price of 10,000 miles = $1,333 * 5 = $6,665. New car math - $2/gal price of 10,000 miles = $1000 * 5 = $5,000. So in 50,000 miles you've saved $1,665. In 50,000 miles you've saved more than half what I saved in 200,000 miles. And the government will pay you another $3,500. $3,500 + $1665 = $5,165. Not bad, but compelling?

Let's say you get greedy and want the $4,000 rebate from the government. (Actually, I think it's more than that. I can't be bothered to look it up.) And you want a pretty sporty car, so you only get a car that gets 25mpg. Old car math stays the same over 50,000 miles. $2/gal price of 10,000 miles = $1,333 * 5 = $6,665. New car math - $2/gal price of 10,000 miles = $800 * 5 = $4,000. So in 50,000 miles you've saved $2,665. $2,665 + $4,000 = $6,665. That's starting to look really nice.

Then there's my friend Jim. He's looking at a hybrid. That will get him 45 mpg. I think his old car gets 15mpg, so we'll go with that. Old car math - $2/gal price of 10,000 miles = $1,333 * 5 = $6,665. New car math - $2/gal price of 10,000 miles = $444 * 5 = $2,220. Over 50,000 miles he can save $4,445.

But that's not where the real savings comes in. The real savings comes in when you look at the price of gas over time. Gas isn't $2/gal. Gas really cost over $4/gal not all that long ago. Consider the following and think of your monthly budget.

How far can you drive on a tank of gas?


size of tank in gallons


10 20 30 40 50
miles per gallon 10 100 200 300 400 500
15 150 300 450 600 750
20 200 400 600 800 1000
25 250 500 750 1000 1250
30 300 600 900 1200 1500
35 350 700 1050 1400 1750
40 400 800 1200 1600 2000
45 450 900 1350 1800 2250
50 500 1000 1500 2000 2500
55 550 1100 1650 2200 2750
60 600 1200 1800 2400 3000
65 650 1300 1950 2600 3250




How much does a tank cost you?

dollars per gallon


1 2 3 4 5
size of tank in gallons 10 $10 $20 $30 $40 $50
15 $15 $30 $45 $60 $75
20 $20 $40 $60 $80 $100
25 $25 $50 $75 $100 $125
30 $30 $60 $90 $120 $150
35 $35 $70 $105 $140 $175
40 $40 $80 $120 $160 $200
45 $45 $90 $135 $180 $225
50 $50 $100 $150 $200 $250
55 $55 $110 $165 $220 $275
60 $60 $120 $180 $240 $300
65 $65 $130 $195 $260 $325

The savings isn't huge, but the higher the price of gas, the less the increase hurts. And that, my friends, is why I'm so glad I bought my hybrid, even if it hasn't saved me all that much.

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