Applied Genius. Maximum Utility.

How to Buy Gas, Part 1

Most people spend a sizeable amount of money on gasoline -- and several hours at the gas station over the course of a year.  Given that fuel economy is on people's minds, let's look at the economics of filling your gas tank.  In particular, how often should you go to the gas station, and how much gas should you buy when you go?

Let's say your time is worth $12 per hour after taxes (probably a serious understatment for most Applied Genius readers, but it makes the calculations work out nicely.)    Your gas tank holds 20 gallons (that's approximately 75.7 liters, for non-US readers.)   Your car gets 25 mpg average fuel economy; you drive 300 miles per week (using 12 gallons per week, even though Virginia Postrel thinks you're a gas hog.)  It takes 5 minutes to do your "gas errand", which includes pulling into the gas station, waiting your turn, pumping gas, flirting with the cashier, getting a cup of coffee (and, heaven forbid, a lottery ticket), etc. 

There is a downside to hauling too much gas around; a gallon of gas weighs 6.2-6.3 pounds, and the US Department of Transportation says that each 125 pounds of extra weight reduces gas mileage by 0.3 mpg.  (I won't translate that into kg and km/l, but you get the idea.)  In addition, let's assume that you expect that gas is going to be cheaper in a few weeks when you next fill up; let's be optimistic and assume that you think that the price-per-gallon will decline $0.01 per day for the next two weeks or so.

In operations management, the technique to solve this problem is called the Efficient Order Quantity (EOQ).  Originally developed in 1915, it came to many managers' attention in 1935(!) via an article in Harvard Business Review.  Economists William Baumol (1952) and (later, Nobel Laureate) James Tobin (1956) used it to estimate how much cash households needed for their day-to-day purchases (and Greg Mankiw once told me a very funny example about how seldom graduate students should use an ATM, in the same vein as this analysis.)  In EOQ terms, the mpg penalty of extra weight is a carrying cost, as is your expectation that gas will be cheaper next week.  Of course, the average driver fills up their tank waaay too often, just as the average student goes to the ATM about 10-15 times as often as is optimal.

Performing an EOQ analysis on this problem indicates that the cost of time spent at the gas station ($1 per stop) is waaaay bigger than the extra cost of a fuller tank, including both the effects of reduced mileage and buying at the high price.   In short, you should wait as long as you can, coast in on empty, and fill 'er up even though you know it'll be cheaper tomorrow.  (Of course, if you're coasting in on empty, you can hardly wait until tomorow unless you have a bus pass, too!)

I should note that you'd be much better off with a larger gas tank (my preliminary calculations indicate that you'd be willing to buy a little more than 74 gallons at a time if your tank could hold that much.)  Even when you buy only 20 gallons at a time, you're acting as if your precious time is worth only $0.85 per hour!  It puzzles me why smaller gas tanks are so popular in new car models; sure, they improve fuel economy, but they positively destroy overall filling-up economy by wasting time.

I should also point out that the 5% rebate on gasoline from a smart credit card is worth $93.60 per year to the consumer in this example, whereas having a magical ability to buy gasoline a little at a time, on an as-needed basis, without spending any time at the gas station (or suffering any fuel-economy penalty) is worth only about $32 per year.  If you haven't succumbed to my blandishments on smart credit cards yet, now would be the time!

Next week I'll be taking a look at how to find good prices for gas (without spending all your time, and gas, cruising around.)   

The Equity Premium Puzzle

Why are investors so afraid of risk?  Sure, it's possible to lose your shirt (and a posterior portion of your anatomy) in the stock market, but don't the rewards outweigh the danger?

A famous economic study on the equity premium puzzle showed that stocks outperform bonds by so much (on average 6% per year) that you would think that investors would choose more stocks than they do.  To quote Wikipedia's version of the common (and ludicrously conservative) tendency, "To quantify the level of risk aversion implied, investors would have to be indifferent between a bet with a 50 percent chance of $50,000 or $100,000 and a certain payoff of $51,209." 

Why are people so averse to taking small risks that they would do the equivalent of "cashing out" for $1,209 over their WORST possible outcome, forgoing a 50% chance of winning $50K?  And (putting on my Applied Evil Genius hat) how can we turn other people's risk extreme aversion to our own advantage? 

How to Spend Money

We all spend a lot of money on everyday purchases, whether we realize it or not.   There is a brand-new credit card designed to reward you for charging those everyday purchases (gas, groceries, and drugstore) rather than using "cash" or some similarly antiquated 20th-century method. 

The new AT&T Universal Rewards MasterCard is the Applied Genius choice, hands-down.  It offers an amazing 5% back in these categories, which is worth nearly $300 the first year alone without any effort at all!   Mycroft carries this card (along with the the Citibank Diamond Preferred Rewards MasterCard and the recently discontinued Chase Cash Plus Rewards Visa, which are similar), and uses it for all his gas, grocery, and drugstore purchases.  He's already persuaded several of his PhD-holding friends to get one of these cards.  You should get it too; here's why.

Save $100 per year on gas.  Gas costs $2.79 a gallon in Applied-Genius land; getting 5% back knocks the effective price down almost $0.15.  You could spend a lot of time driving around to find gas at $2.65, or you could just whip out your AT&T Universal Rewards Card.  If you consume 12 gallons of gas per week the way Mycroft does, that's worth about $2 per week, or nearly $100 per year just for the gas rebate.  But wait, there's more.

Save $100 per year on food.  Groceries and drugstore purchases also qualify for the 5% rebate.  According to the USDA, the typical US household spends 5.4% of its disposable income on food at home.  This amounts to approximately $2000 per US adult per year.  (If you're reading Applied Genius, it's probably higher than that.)  Guess what?  5% of $2000 is another $100 per year, just for the food rebate.  It's $200 per year if you buy groceries for two adults, $300 per year for three, and so on.  But wait, there's more.

Get $100 Free Money to Start.  Citibank (the issuer of the AT&T card) also gives back 1% on all other purchases, which you can get from other cards, too.  With AT&T Universal Rewards, you can take this rebate as cash on your statement (which is taxable) or as gift cards at many merchants (which, let's just say, "doesn't get automatically reported as income to the IRS on a 1099-MISC.")  As if this weren't enough, Citi will give you $100 to start off with, after your first purchase.  But wait, there's more.

Earn $270 or more in Free Interest.  Lots of cards offer introductory "teaser" balance transfers.  The AT&T Universal Rewards Card and the recently discontinued Chase Cash Plus Rewards card are unusual in that it gives you 0% APR on all purchases for the first 12 months.  As you rack up charges for your everyday purchases, simply pay the minimum monthly payment -- and defer the rest until 2007 with no interest charged.  If you're really ambitious, you could deposit the rest of the money into a high-yield savings account (such as offered by Citibank, HSBC, or Emigrant Direct) to earn 4.5%, risk-free, for a year on money you've already spent.   If you spend $1,000 per month, this translates into a $270 gain in free interest alone.    If you spend more (especially early in the year), you gain even more. 

Total Benefit:  $650 the first year. After you pay off your whopping bill at the end of the year, having racked up rebates the whole time -- $100 for spending $2K on gas, $100 for spending $2K on food, $100 free for signing up, $80 for the 1% rebates on the other $8K of stuff you bought, and $270 of free money from the 0% offer --  you'll have $650 to splurge with.  (You could even buy some fluorescent light bulbs for an official Applied Genius parlay, turning $40 into $1400.)   You can earn up to $300 each year after the first, a common cap in the industry.  If you're a really big spenda, I understand Emigrant Direct has a capless 1.4% rewards card, which would be worth only $196 to our example consumer but would be worth more if you spent more than $46,428 on your card (thanks to reader J.E. for the tip.)

Now how much would you pay?  Since you're reading Applied Genius, instead of Clueless Idiot, you already know that there's no annual fee.   (Forbes has a list of very high annual-fee cards, which cause Mycroft to shake his head in wonder.)

You'll find a tasteful link on the left (and a really, really garish link at the bottom of the post.)   You're welcome to try to apply for the Chase Cash Plus Rewards Visa (our old recommendation), which is being phased out; please call 1-888-787-0329, or apply for one of the other Citibank cards that also give 5% on gas, groceries, and drugstores listed on the left (which are very close substitutes.)

(In the interests of full disclosure, I'd like to remind you that Citi will, indeed, pay us if you sign up directly through us.  And wouldn't your significant other, sibling, or parents like one, too, with their very own free $100 to start?)

The Best Investment Ever

Fluorescent light bulbs have been around for a long time, but there are still a lot of households that don't use them.  They should. 

Let's do a back-of-the-envelope calculation about how much one of these bulbs is worth.

Assume that we replace a traditional 100-watt traditional incandescent bulb with a 23-watt fluorescent bulb.  The traditional bulb costs $0.50 and lasts for 2,000 hours of light, whereas the fluorescent bulb costs $X and gives 10,000 hours of light.   Electricity in Applied-Genius land costs $0.135 per kilowatt-hour these days (twice the 1999 rate!)  Finally, assume for the sake of argument that you're flat broke and would have to buy the bulbs on your credit card, paying 20% APR for the privilege.  Solving for the price $X that exactly equalizes the cost of doing it the old incandescent-bulb way vs. the new fluorescent-bulb way gives us the Net Present Value of buying an incandescent bulb.

The Net Present Value of buying a fluorescent bulb under these assumptions is -- ready? -- a little over $72.  For each bulb.  If your money's worth only 8%, the NPV rises to $90+.   For each bulb.

At Amazon, these 100-watt replacements are $17 for a 4-pack.  At these prices, your NPV exceeds your cost for an gain of $271 per 4-pack.  In other words, buying a houseful (20 bulbs) is like winning $1355 in the lottery (and you don't even need to pay taxes on it!)  And that's ASSUMING that you need to pay the outrageous 20% interest on your card.

Another way to look at the attractiveness of this investments is the Internal Rate of Return (IRR) method.   A $10 bulb returns 172% annually on your investment.  A $6 bulb returns 232%; a $4.25 bulb returns 248%, and a $1 bulb returns a whopping 555%.  Note that these bulbs are frequently available in dollar stores, as well as at Big Lots and other discount retailers; brand-name GE bulbs are available at Sam's Club for approximately $3 each.  (Canadian dollar stores even offer entry-level Sunbeam fluorescent bulbs for $1 Canadian, and their electricity rates are higher than in the USA.)   

Note that these are far, far better returns than Warren Buffett has gotten at Berkshire Hathaway, and basically risk-free (and tax-free) to boot.  I suspect that Warren, a legendarily sensible sort of fellow,  knows about fluorescent lights, and may even have a few in his Omaha childhood home; he'd undoubtedly invest billions in 248%-return risk- and tax-free ventures if they were made available.

(The Applied Genius Bulb Spreadsheet allows you to do these calculations for your situation, including your local electricity rates and the number of hours per day that you use the light.)

Just to beat the already-dead horse to death and beyond, there are a few additional and important (but difficult-to-quantify) benefits as well.

(a) If you air-condition your home, you should realize that you're paying close to twice as much, because most of the energy used by a traditional incandescent bulb is thrown off as heat.  You pay twice for that energy:  first when it's emitted from the bulb, and again when your air conditioner spits it out of your house.

(b) Fluorescent lights don't require changing nearly as often. You'll spend less time on a ladder changing hard-to-reach bulbs, as well as less time at the store buying them.  (Interestingly enough, it's this maintenance-cost savings which drove adoption of fluorescents in commercial buildings, not the power savings.)

(c) Saving electric power means slower increases for future electric power prices.  (OK,  you're sharing this benefit with everyone in the world, so the direct effect on your own electric bill of you choosing fluorescents is really, really small.  But you can feel good about it, knowing that you're in harmony with the first formulation of Kant's Categorical Imperative, which is often inaccurately equated with the Golden Rule but can be better paraphrased as "Do only that which you wish everyone would do.")

(d)  Last but not least, you can brag to your friends about how smart you are.  (But you should, eventually, 'fess up and tell 'em where you read about the business case for fluorescents.)

Get thee to the bulbery!