Political Calculations
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September 30, 2009

S&P 500 Average Monthly Index Value and Prediction Track, January 2008 into October 2009 How much does the base value for projecting the future value of stock prices matter?

That's the question we're asking this morning as we consider where the S&P 500 might go in October 2009. Throughout most of this year, stock prices have more or less paced the "blue track" shown in the chart to the right, which represents the lower half of our full forecast range [1], as determined by our math.

Acclerations of S&P 50 Average Monthly Index Value and Trailing Year Dividends per Share (and Futures), January 2001 through September 2009 But now, we wonder if investors might look at how far stock prices dropped in October 2008 and say: "that's not a realistic base from which to project today's stock prices." After all, the period from late September 2008 through October 2008 marked the beginning of the meltdown in the financials, which represented a very large part of the market capitalization of the S&P 500.

So we created an alternate track - one that resets the base for projecting future stock prices to September 2008, which appears to have been close to being on target for where stock prices will have gone in September 2009 [2], with respect to our full typical forecast range.

And we'll find out at the end of October is our fork in the road has taken stock prices to Door A, Door B, or some other door altogether.

Unless the stock market decides to take Yogi Berra's directions [3]....

Notes

[1] Our full target range is generally based on an amplification factor of 7.0 for the low end and 11.0 for the high end, which is consistent with our observations of the degree to which changes in the future expected growth rate of the S&P 500's trailing year dividends per share drive changes in the growth rate of stock prices since 2001. An amplification factor of 9.0 coincides with the middle of the full target range. Beginning in September 2009, we lowered the amplification factor we use for the low end of our forecasting to 6.5, as a more direct method of accounting for the slow erosion we've observed in the growth rate of dividends throughout this year - prior to that change, we would simply round the calculated boundaries of our forecast range to the nearest whole multiple of "5".

[2] We were off target on our original forecast for September 2009, as we initially anticipated that the period from 10 September through 16 September would be one in which stock prices would fall. Fortunately for our plus/minus score, we dug into the numbers and realized that stock prices would instead soar above our originally predicted range, a finding we incorporated into our September forecast post as an update on 10 September. We'll be updating our plus-minus score for predictions in mid-October.

[3] Yogi directions are: "When you come to a fork in the road, take it." The story behind Yogi's quote from Wikiquote:

Berra says this is part of driving directions to his house in Montclair, New Jersey. There is a fork in the road, and whichever way you take, you will get to his house.

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September 29, 2009

Shadowy Figures Around Caduceus - Source: VA.gov Did you know that Americans who don't have health insurance are more than twice as likely to be killed, literally, than those who do have health insurance?

Here's how we know. Starting with the spreadsheet data that the FBI provides for the number of violent crimes and homicides in the U.S. each year, we can combine that information with data collected by the Bureau of Justice Statistics for the percent of victimizations in which the victims had health insurance or were covered by government health programs for its annual survey of Criminal Victimization in the United States (in Table 78). Using these two sources of data, we can work out how many victims of personal crimes of violence had health insurance and how many did not.

Number Violent Crimes in U.S., 1992-2008, with Number of Uninsured Victims, Actual vs Predicted Better yet, we can take the U.S. Census Bureau's data on the number of individuals in the United States there are without health insurance and use that information to predict how many victims of criminal violence there should be and compare it with the actual results.

Our first graph shows what we found. For the years from 1992 through 2006, the last year for which we have the health insurance status data for violent crime victims, we find that the number of uninsured victims of violent crimes are more than twice as often found to be the victim of a personal crime of violence than the what would be predicted using the U.S. Census' data on the total number of those counted as being without health insurance!

Number Violent Crimes in U.S., 1992-2008, with Number of Uninsured Victims, Estimated vs Predicted So we took it to the next step. Using the data for the number of homicides and non-negligent manslaughters recorded in the U.S. for each of these years, we assumed that the same percentages would apply for this class of victim. With these assumptions, we would estimate that the number of victims of intentional murder or manslaughter and who do not have health insurance represent more than a third of the total number of intentional murderous assault by others.

Why does this matter? Well, this finding allows us to debunk some potential junk science related to the current debate on the U.S. health care system

Here, a 2009 study on Health Insurance and Mortality in US Adults by Andrew P. Wilper, Steffie Woolhandler, Karen E. Lasser, Danny McCormick, David H. Bor and David U. Himmelstein offers the following summary:

Objectives. A 1993 study found a 25% higher risk of death among uninsured compared with privately insured adults. We analyzed the relationship between uninsurance and death with more recent data.

Methods. We conducted a survival analysis with data from the Third National Health and Nutrition Examination Survey. We analyzed participants aged 17 to 64 years to determine whether uninsurance at the time of interview predicted death.

Results. Among all participants, 3.1% (95% confidence interval [CI]=2.5%, 3.7%) died. The hazard ratio for mortality among the uninsured compared with the insured, with adjustment for age and gender only was 1.80 (95% CI=1.44, 2.26). After additional adjustment for race/ethnicity, income, education, self- and physician-rated health status, body mass index, leisure exercise, smoking, and regular alcohol use, the uninsured were more likely to die (hazard ratio=1.40; 95% CI=1.06, 1.84) than those with insurance.

Conclusions. Uninsurance is associated with mortality. The strength of that association appears similar to that from a study that evaluated data from the mid-1980s, despite changes in medical therapeutics and the demography of the uninsured since that time.

Do you see where they likely botched it?

They didn't control for cause of death! Since those without health insurance are estimated to be more likely to die as the result of injuries inflicted by external agents (like murderers), not compensating for that difference will skew the results of this kind of study in a way that suggests that these individuals lack of health insurance is a serious contributing factor to their disproportionately larger share of deaths.

But the last time we checked, things like homicide, while accounting for a portion of the total number of deaths in any given year, are completely independent of whether the affected individual had access to health care or health care insurance.

Through 2007, we know that non-health related causes of death account like these account for 4.2% of the total number of deaths observed in the NHANES III survey population of 33,994 individuals of age two months or older, or 141 out of 3,384 deaths.

Of these, 18 were victims of homicide, 23 died as a result of suicide, 26 died from injuries sustained in falls, and 45 died as a result of motor vehicle accidents.

How much do you want to bet that these factors account for a good portion of the disparity "observed" in the Harvard study?

Considering the Harvard study's population subset of 9004 individuals within the NHANES III survey that ran from 1988 through 1994, 16.2% (2350) were without health insurance. Of the 351 individuals within the group of 9004 who died by the Year 2000 follow up, 17.2% (or roughly 60 individuals) did not have health insurance. Using the 16.2% figure for the entire population and multiplying it by 351, we would predict that 57 individuals without health insurance would have died. This outcome suggests that the Harvard researchers' conclusions are largely based on seeing three more deaths than would be predicted for the uninsured subset of their sample.

How likely is it that these three "extra" deaths might fall into the "non-health related" cause of death category?

Then again, maybe the whole exercise is moot. Since the NHANES III survey is a cross-sectional study rather than a randomized, controlled clinical trial, it's really not possible to draw any real conclusions from findings based on the survey's data. Instead, the best you can get are indications of where future research might be valuable.

And by indicating that the uninsured are 40% more likely than the insured to die, how likely might it be that a team of Harvard researchers will be able to get the funding they need to research it further?

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September 28, 2009

Our hats are tipped to James Grant and Todd Spencer of Uniform Chaos - they've visualized various financial aspects of the component stocks of the S&P 500 as if they were planets orbiting a solar system! Here's the video introducing some of the capabilities of their data visualization approach (via Barry Ritholtz):

Previously on Political Calculations

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September 25, 2009

Carnival Midway from The Jerk Welcome to the Friday, September 25, 2009 edition of On the Moneyed Midways! Each week, we select the top posts we find in the best of the business and money-related blog carnivals, which we present here, in one place, to kick off your weekend reading!

But we're not the only game in town anymore! The Best of Money Carnival does something very similar: every two weeks, they ask a number of well-established bloggers who regularly post on money-related topics to submit their best post, from which the top ten are selected for inclusion in the biweekly edition of the "Best of Money" carnival.

That makes it more of a true blog carnival than OMM. By our definition, we're more of an ubercarnival, since we don't directly solicit bloggers for their contributions, instead reviewing all the posts that they've contributed to other blog carnivals.

So are we threatened by the competition? No way! As we see it, there's a very limited supply of top notch writing and commentary in the blogosphere (it's even more limited in legacy media), so calling more attention to the best stuff out there is only beneficial.

Now, onto the best posts we found in the week that was....

On the Moneyed Midways for September 25, 2009
Carnival Post Blog Comments
Carnival of Personal Finance Why Rechargeable Batteries Are Rarely Cost Effective Len Penzo dot Com The Best Post of the Week, Anywhere! It's not often that we come across a single blog post that greatly increases our knowledge of a topic, but Len Penzo's take on when and where rechargeable batteries make sense to use does just that!
Carnival of Real Estate Huntington National Bank: Are Your Freaking Kidding Me? From Deep With the WTF Files Phoenix Real Estate Guy Jay Thompson tees off on the conditions that financially-strapped Huntington National Bank is requiring of potential homeowners before it will even review their mortgage application. We note that many of these policies would not seem to be shared by healthy institutions.
Cavalcade of Risk How Much Term Life Insurance Do You Need? Good Financial Cents Jeff Rose works through the math needed to figure out just how much life insurance you need. We predict Jeff's math will become a tool here sometime in the near future!...
Festival of Frugality Guide to Getting Hired Quickly My Life ROI MLR extracts the key lessons to learn from a CNN article describing how a computer programmer who was given a month's notice before being laid off was able to start a new job after just three days of unemployment. In the current economy.
Money Hacks Carnival Our Natural Disaster Story and Lessons Buck$ome Boomer's Journey to Retirement Two years ago, a neighbor knocked on Bucksome's door to let them know their neighborhood was being evacuated because of a fire. Here, she describes what she and her husband have done since to be better prepared to react to a natural disaster.
Carnival of Pecuniary Delights 25 Traits of the Not So Well To Do Free From Broke FFB offers her observations of the things that seem to go hand in hand with being strapped for cash.
Best of Money Carnival Best of Money Carnival Steadfast Finances OMG - we have competition! Best of Money tweaks our formula by going straight to the business and personal finance bloggers themselves to nominate their best posts from the previous two weeks, then picks the 10 best of all the contributions. Absolutely essential reading!, and your independent confirmation that we're not alone in selecting many of the posts we pick as being among the best!

Previous Editions

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September 24, 2009

Crystal Ball If you were in the public prediction making business back in 1993, could you have accurately predicted where technology would go? Or described where technological change would take us a little over 16 years later?

Now, what if you were part of the marketing team for AT&T? What are the odds that you could reasonably describe what the world of tomorrow would look like in the early days of the World Wide Web?

And what if you committed that vision to a series of television advertisements narrated by Tom Selleck?

We here at Political Calculations are pleased to bring you, via Robot Dreams, via Core77, the future according to AT&T's advertising team of 1993!

We wondered what other predictions made in 1993 might be happening today. Here are three of the more amazing ones:

Michael Crichton, Vindicated

Jack Shafer writes:

In 1993, novelist Michael Crichton riled the news business with a Wired magazine essay titled "Mediasaurus," in which he prophesied the death of the mass media—specifically the New York Times and the commercial networks. "Vanished, without a trace," he wrote.

The mediasaurs had about a decade to live, he wrote, before technological advances—"artificial intelligence agents roaming the databases, downloading stuff I am interested in, and assembling for me a front page"—swept them under. Shedding no tears, Crichton wrote that the shoddy mass media deserved its deadly fate.

The Clash of Civilizations?

Samuel Phillips Huntington (born April 18, 1927) is a political scientist known for his analysis of the relationship between the military and the civil government, his investigation of coup d'etats and his thesis that 'the fundamental source of conflict in this new world will not be primarily ideological or primarily economic. The great divisions among humankind and the dominating source of conflict will be cultural. Nation states will remain the most powerful actors in world affairs, but the principal conflicts of global politics will occur between nations and groups of different civilizations. The clash of civilizations will dominate global politics. The fault lines between civilizations will be the battle lines of the future.' [Source: EconomicExpert.com]

The Coming Technological Singularity

Vernor Vinge (pronounced VIN-jee, rhyming with 'stingy') (born February 10, 1944) is a mathematician, computer scientist and science fiction author who is best known for his Hugo award-winning novel A Fire Upon the Deep and this 1993 essay, in which he predicts an imminent acceleration of progress caused by increasing speed of computers and developments in artificial intelligence. [Source: EconomicExpert.com]

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September 23, 2009

Solar Panel Installation on Roof - Source: neo.ne.govHave you seen your power bill lately? Are you happy with it?

If like many people, you have and you're not, to answer both questions in order, perhaps you might find the appeal of saving the money you currently send to the power utility companies each month by generating your own power directly from the sun to be a pretty compelling idea.

And why not? It's a technology that can provide the energy you want while cutting your bill and is currently believed to be good for the environment (you know environmentalists - sooner or later, they'll find something wrong with it.)

But does it make sense to go solar?

Warren Meyer has been weighing the costs and benefits of going solar at his home in Phoenix, Arizona, perhaps the sunniest major city in the United States. If going solar can be made to work economically anywhere in the U.S., Phoenix would be at the top of the list of places that would benefit. He found that going solar could work, but only if U.S. and Arizona taxpayers chipped in and helped him. A lot:

For this analysis, I will use the prices here. The $72,167 cost for a 11.76 kW system is pretty competitive at $6.13 per watt installed (this is rated watts, not actual — see footnote). The panels themselves can be bought for about $3 per watt, with about $1 a watt for other equipment like inverters and $2 per watt for installation. Do-it-yourself packages for a similar size system are here and go for around $4-$4.50 per watt.

The solar company estimates that this system in Phoenix will save me$2,779 a year on my electric bill. I have not checked their math, but I assume they are not under-estimating this number in their marketing literature. Taking this savings, we get a payback on the installation of about 26 years. This ignores future electricity price increases, but also ignores the time value of money. At 8% over 20 years, it has a net present value of NEGATIVE $41,558. At the end of the day, this is a terrible return — in fact a huge value destruction.

But I began this post saying a solar investment might make sense. How? Well, that is where your willingness to reach into your neighbor’s pocket comes in. Our solar company estimates the following tax breaks and rebates on the system described above:

  • Utility rebate: $35,280
  • State income tax credit: $1,000
  • Federal income tax credit: $21,650

So, in building this $72,167 improvement on my house, I get to use $57,930 of other peoples’ money**. As Steve Martin says in The Jerk: "That takes the pressure off!"

Like in many other cases, other peoples' money suddenly makes solar a good investment. Now we are looking at $2,779 a year in savings from a net investment of $14,237, or about a five year payback. Over 20 years even assuming no inflation and an 8% cost of money that has an NPV of $12,081.

So — I officially reverse my past conclusions that home solar does not pay. It can in fact be a good investment — for you.

We wondered about that math however. What if utilities increase their rates over time? Wouldn't that make going solar today more beneficial, since the potential savings would grow over time as well?

The most recent trend we can find for Phoenix indicates that the cost to consumers of buying electricity has been rising steadily for years. In a series of general rate increases from 2002 to 2008, Arizona utility SRP increased the rate it charges its customers by 26.7% in three separate increases, which suggests an average compound annualized rate of increase of 4.0%.

If that rate of increase continues, that could be a pretty significant savings for a homeowner going solar. We next went to SRP's web site to find out what kind of deal we might be able to get through them. Here's what we found:

Solar electric system

When you install a solar electric system, SRP will help defray your cost with an incentive of $2.70 per watt, up to $13,500 (through April 30, 2010). Here's an example of the costs and incentives associated with the installation of a system:

Size Typical cost1 SRP solar incentive Arizona tax credit2 Federal tax credit3 Net cost Annual savings4 Simple payback
5 kW $35,000 $13,500 $1,000 $6,450 $14,050 $720 20 years
  1. Costs may vary depending upon the contractor and materials you select.
  2. The Arizona tax credit is 25% of the cost, capped at $1,000.
  3. The federal tax credit is 30% of cost, less the SRP incentive.
  4. Savings are calculated based on an annual solar energy production of 1,600 kWh per kW-DC at $0.09 per kWh, and will vary based on the size of the system installed, orientation and energy consumption.

Sure, it's not the 11.76 kW system that Warren investigated, but let's say this 5.00 kW system offered by the utility company suits our Phoenix homeowner's needs. We'll assume that the utility rate goes up by 4.0% per year, which means the annual benefits provided by the system would steadily increase in value by that amount.

On the other side of that coin however is the effect of depreciation - the fact that any system we might choose to install will decrease in value over time. Here, we'll assume that all the incentives and tax credits for installing the system are enough to offset much of the effects of depreciation that the system will have over its lifetime. Since those subsidies reduce the cost of the system by $20,950, or almost 60% of its original value, we'll assume that the unit depreciates in value at a steady rate of 1.0% per year over its useful life, which we'll assume also incorporates the costs of maintaining the system. So, after 20 years, the unit would be worth 20% of its original value.

We'll note that losing 80% of its value over a 20 year period is equivalent to a straight line depreciation of 4.0% per year. Without the subsidies, the effects of depreciation would completely cancel out the benefits of increased savings of energy costs. For our purposes though, we care about the net rate of appreciation, which we find as the difference between the rate at which the benefits increase each year and our assumed rate of depreciation: 4.0% - 1.0%, or 3.0%.

Finally, there's the issue of the cost of money over time. Here, we'll assume that cost is reflected by the average rate of a home equity loan, such as a homeowner might take out for the purpose of raising the cash needed to cover their costs of installing the system. From Bankrate.com, we found an average 8.228% rate for home equity loans in the Phoenix-Mesa market, which we'll use as our cost of money.

Does solar make more sense now? Let's find out:

Home Solar Generating System Data
Input Data Values
First Year Savings
Cost of Buying and Installing System
Net Rate of Appreciation [%]
Cost of Money [%]


How Profitable Is It to Go Solar?
Calculated Results Values
Profitability [%]

Using our default data, we find that in terms of profitability, our hypothetical homeowner would nearly break even.

We find then that installing the system just barely makes sense for our hypothetical Phoenix homeowner, especially if they can reasonably expect that their power bills might go up at a faster rate over time or if they can get a lower cost of money.

But let's not forget the taxpayers and the utility company! It costs them $20,950 to obtain the same benefits for the homeowner. Replacing the default data for the Cost of Buying and Installing System with figure reveals that they are underwater in this deal to the extent of -1.8%.

As a result, we find that with currently available technology, even in Phoenix, Arizona, the one major city in the U.S. where it would provide the biggest bang for the buck, and even with massive subsidies, going solar for homeowners is overall a losing proposition.

Warren Meyer came to a similar conclusion for his considerations:

For the country, it is a terrible investment. Your neighbors are contributing $57,930 in subsidies while you receive just $12,081 in benefits. The remainder, just over $45,000, is a dead-weight loss to the economy. It is money destroyed by the government.

This is surprisingly like the ethics problem of pulling a lever to get a million dollars but someone you don’t know in China dies. The only difference is that you get $12,000 and someone you don’t know loses $58,000.

You're more than welcome to use our tool above to determine if the technology you're considering is worth it for you.

For our part, we played with the numbers and found that a system that can produce $720.00 in annual savings, with a net rate of appreciation of 0.0% (assuming the increase in annual savings and depreciation balance each other out) and at the same cost of money would need to cost just $8,750 to buy and install for the homeowner to break even. Such a system would not create any deadweight loss or produce any distortions into the economy through subsidies, as they would not be needed.

Clearly, politicians seeking to create or enhance such subsidies have other priorities....

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September 22, 2009

In June, we entered PJTV's Generational Theft contest. In August, we had made the first cut and went into the second round of judging. Yesterday, PJTV announced the winners: Hartford, Connecticut-based Trinity College's senior Gavin Romm and professor Edward Stringham.

From what we know from the contest administrators, our entry came in second place overall.

But we don't feel bad about that! Here is the spreadsheet they created, here are sample screen shots of their basic results and here is PJTV's Allen Barton's video interview of the contest winners (click the image to access PJTV's web video):

PJTV Generational Theft Contest Winners

From the interview, we believe we can tell where our entry likely fell short in the final point count: we simplified the user input too far.

Here, in creating our web-based tool, we took all the different stimulus and bailout-driven debts the government has taken on since 2008 and condensed it into a single figure, while also embedding it directly in our tool's programming code for the sake of keeping the user interface very simple. This approach, combined with our analysis, allowed us to simplify the data entry portion of our tool to just two elements: a 2009 college graduate's starting income and a year for which to project the personal impact of all the government's massive new spending.

While that's an advantage for a web-based tool, this approach de-emphasizes the individual components of that debt, which we believe became a deciding factor in the contest judges criteria for the winning entry. Contest winners Romm and Stringham's Excel spreadsheet, makes each of these components more visible, although with the trade off of greater complexity. Plus, the choice of using Excel allows for graphs to be part of their tool's output, which we think also gave Romm and Stringham an edge in the judging.

For their efforts, Romm and Stringham have each won $10,000, to which we say: Congratulations!

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September 18, 2009

Carnival Midway from The Jerk Welcome to the Friday, September 18, 2009 edition of On the Moneyed Midways, where each week, we bring the best posts we found among the best of the week's business and somehow money-related blog carnivals!

What a weird week! In reading through all the carnivals, we actually lost track of how many times we read a guest post - or in other words, a blog post written by somebody other than the blogger who's site we were visiting!

It was then even weirder when we found the guest posts were often far better than the other week's posts contributed to our survey of blog carnivals by the regular authors behind their own blogs!

We're not going to knock it - there are obviously some very good bloggers out there who recognize good writing when they see it and who are willing to give it a platform when they need a break.

Don't take our word for it - see for yourself what we found to be the best posts of the week that was....

On the Moneyed Midways for September 18, 2009
Carnival Post Blog Comments
Carnival of Debt Reduction Sweathing the Big Stuff http://www.getrichslowly.org/blog/ Guest blogger Sierra Black discusses how she made a big change to save big money - which has made it possible to start reduce her family's big debts in a way where she can see the light at the end of the tunnel for the first time.
Carnival of HR Carrots Suck, Give Me Bacon! Punk Rock HR The Best Post of the Week, Anywhere! Lance Haun guest posts with his take on "carrot" incentive programs, many of which he sees as a weak substitute for real leadership. His "Bacon Method" is right on the money!
Carnival of Personal Finance Cigarettes vs. Coffee - Which Is Financially Worse for You? Budgets Are $exy Let's say you've got two certain habits. Getting rid of one of them might save you a lot of money. J. Money does the math and tells you which one it is!
Carnival of Real Estate Invite the Neighbors to Your Open House Arch City Homes Many, and possibly most, realtors despise holding open houses since they mainly attract people who already live in the neighborhood who aren't looking for a house. Karen Goodman turns that conventional wisdom around and says it pays to bring as many neighbors in as you can!
Carnival of Trust Selling the Invisible: How People Buy Something They Don't Understand Jobing South Florida Community Blog Jorge Lazaro Diaz discusses how to build trust with customers when all they know of what you do is what they see. Absolutely essential reading!
Festival of Frugality How to Eat Healthy on $10 a Day Bargaineering Vic Magary guest posts his strategy for dining on a healthy diet and keeping the grocery bills down!
Carnival of Money Stories Off My Giving List Free Money Finance FMF is tired of all those pestering calls soliciting charitable donations over the phone. Here, he describes how one organization wrecked any chance of ever receiving a donation by not listening.

Previous Editions

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September 17, 2009

Following John Whitehead's example, we're tapping our e-mail inbox today as a source of inspiration for what to post about today. And what a doozy we have! It seems that we've unintentionally provoked an angry reaction to our post considering the cost of breastfeeding versus formula. Our agitated reader, Michelle, writes:

In regards to the blogpost at: http://politicalcalculations.blogspot.com/2009/04/cost-of-breastfeeding-vs-formula.html, I believe there is a major flaw -- a biased one at that -- in your calculations. Why do you not include the time it takes to shop for, mix, and prepare formula? What about the cost for bottles, nipples, cleaning utensils? The time and resources (i.e., water) to clean the bottles afterwards? Why do you also not include the time it takes to feed an infant with formula, too? Does it just magically get from the bottle into the baby's belly somehow without taking time? I believe you only include the time factor for breastfeeding to try to strengthen your argument, which I believe is weaker than the argument for breastfeeding. I believe the burden of proof is on you to disprove the theory that breastfeeding is a better source of nutrition for an infant than human milk substitute. Prove that formula feeding is better! Do you really believe that something manmade (human milk substitute) from cows or plants is as good or superior to something human-made just for humans? If so, you've been duped by the manipulative advertising of the formula companies. I don't see your evaluation of the evidence FOR formula-feeding. If you're a true scientist, economist, mathemetician, whatever you are...then you would present the full possibilities in your calculations. It's otherwise completely biased in the favor (or at least I see that's the point here) of your flawed point of view. (And is it really necessary to put a link to other sites for the term "breastfeeding nazi"? That just proves the point that you are not a reliable source of information.)

Fair enough. Let's consider Michelle's major points one by one....

Why do you not include the time it takes to shop for, mix, and prepare formula? What about the cost for bottles, nipples, cleaning utensils? The time and resources (i.e., water) to clean the bottles afterwards?

We also didn't consider the time it takes to shop for, mix and prepare the long-well established additional 600 calories of food per a day that a mother requires to breastfeed her child. Or the cost of dishes, cups and eating utensils used by the breastfeeding mother. Or the time and resources (i.e., water) to clean the dishes afterward.

Although we suspect these things would have equivalent expenses in terms of both cost and time to the comparable activities associated with the use of infant formula, it's quite possible that the expenses associated with breastfeeding are higher.

Why do you also not include the time it takes to feed an infant with formula, too? Does it just magically get from the bottle into the baby's belly somehow without taking time? I believe you only include the time factor for breastfeeding to try to strengthen your argument, which I believe is weaker than the argument for breastfeeding.

As we didn't have any data at the time to apply otherwise, we assumed that the time required for the child to consume formula is the same as that required for the child to breastfeed, which makes for a very direct comparison. As a result, the "savings per hour breastfeeding" figure provided by the tool is the savings that result from not using formula.

Then again, what if Michelle might be right? It could well be possible that formula-fed babies are faster eaters than their breastfed counterparts, which would reduce the savings per hour spent breastfeeding, thereby making formula more attractive.

I believe the burden of proof is on you to disprove the theory that breastfeeding is a better source of nutrition for an infant than human milk substitute. Prove that formula feeding is better!

One cannot "disprove" a theory, as one cannot prove a negative contention. This would be called "junk science." Fortunately, Michelle recognizes this and calls for formula feeding to be proven better.

Unfortunately for Michelle, formula doesn't have to be "proven better" to justify its use from a nutritional standpoint. Formula would only need to be "nearly nutritionally equivalent" to breast milk to justify its use in place of breast milk. Likewise, breast milk would only need to be "nearly nutritionally equivalent" to formula to justify its use in place of formula.

Do you really believe that something manmade (human milk substitute) from cows or plants is as good or superior to something human-made just for humans?

We're presuming from her statement that Michelle believes that men aren't humans, as she implies that something "man"-made is less desirable than something "human"-made. But we'll give her the benefit of the doubt and assume her hateful language dehumanizing men is really just confused rather than being reflective of a highly sexist outlook on life.

As for the source of the nutritive content of infant formula versus breast milk, we wonder if cows or plants might not be part of a breastfeeding mother's diet? In which case, is a breastfeeding mother really adding serious nutritional content to the breast milk or just processing the real nutrition into something her infant can consume. Much as infant formula producers do through other methods that have demonstrably evolved and improved over time.

We don't know the answer to that question. We doubt Michelle does either. We think that we can agree that babies should be fed, although we can't speak for Michelle, who might differ from our view on the basis of gender.

If so, you've been duped by the manipulative advertising of the formula companies. I don't see your evaluation of the evidence FOR formula-feeding.

We're not aware of having seen any advertising of any kind from those "manipulative" formula companies. Perhaps they're sending us subliminal messages? Evil bastards.

Then again, we believe our evaluation pretty obviously considered the cost of using infant formula with respect to breastfeeding, which Michelle seems to have forgotten by this point of her e-mail.

If you're a true scientist, economist, mathemetician, whatever you are...then you would present the full possibilities in your calculations.

We understand your confusion in this area. But we can assure you that while Ironman defies categorization, Ironman does work to ensure the full range of relevant possibilities are included in the calculations presented on the site. What's more, if you don't like those presented assumptions, you have the ability to alter them in the tools provided with them.

It's otherwise completely biased in the favor (or at least I see that's the point here) of your flawed point of view. (And is it really necessary to put a link to other sites for the term "breastfeeding nazi"? That just proves the point that you are not a reliable source of information.)

To see what to which Michelle is referring, here's the relevant text of our post in context, with the link (aka "free speech") that Michelle advocates be suppressed:

But more than that, those declines exist over time even as there's an amazing amount of social pressure put upon mothers to breastfeed in the U.S., including increasing levels of government-backed pressure to impose and enforce the practice on mothers.

But are they justified? Does the data back up these activists and public officials? Or are they just being a bunch of breastfeeding nazis?

We admit that linking to a Google search of the term "breastfeeding nazis" is perhaps less than optimal. We should have instead linked to the top post returned in that search which explains the 5 Things That Make You a Breastfeeding Nazi... And 5 Things That Don't.

We'll leave it as an exercise to our remaining readers (Goodbye Michelle!) to determine for themselves how, and to whom, the term might be properly applied.

Update: We might have to do this more often - compared to the usual kind of post we do, we can bang this kind of thing right out!

On second thought, maybe not - we said goodbye to one reader today - we really don't want to alienate the other three....

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September 16, 2009

With stock prices rallying strongly today, we thought we'd take the opportunity to consider where the money that's going into stocks today is originating. Reuters' Matthew Goldstein reports (as of 12:18 PM EDT):

NEW YORK (Reuters) - The S&P 500 and Nasdaq both jumped 1 percent on Wednesday as increased industrial production and a pickup in mergers and acquisitions reinforced hopes the economy was gaining speed.

Commodity prices rose, with gold hitting an 18-month high, and boosted natural resource companies like Freeport-McMoran Copper & Gold Inc (FCX.N), up 1.6 percent to $72.49.

Software maker Adobe Systems Inc said it will buy Omniture, a company that makes software to analyze Web traffic, in a bid to boost sagging sales.

Industrial output advanced for a second consecutive month in August, while higher gasoline costs pushed up consumer prices, although economists said the risk of inflation remained low.

Wall Street Bull (Source: FBI) The increase industrial output is a nice and welcome change, but in our view, it is not a market driving change at this point in time.

Meanwhile, we also reject the "increase" in mergers and acquisition (M&A) activity as a serious source of upward market momentum because of the companies involved. Adobe Systems is #118 when it comes to market capitalization weighting in the S&P 500, while Omniture isn't big enough to even make it into the list. A change in Adobe's stock price could affect the value of the the overall index, but not by very much and, as Goldstein observes, its stock price went down. Consequently, we find that particular news isn't behind today's rise in stock prices.

On the third count, Goldstein reports that gold, commodity and gasoline prices are up, as are their related stocks, but that inflation risks are low. That suggests that the U.S. dollar has lost some more value. Good for industrial output, as U.S. produced goods become more competitive in the global market, but as we noted earlier, that factor is not a huge market driving change.

Looking at the component stocks of the Dow Jones Industrial index today, we find that index' two oil companies, Exxon Mobil (#1 in market cap for the S&P 500) and Chevron (#11), are only seeing their stock rise in value by roughly 1.25% (at this writing). But we see that other large companies are seeing their stock prices rise by much larger percentages, such as General Electric (#3) by 6%, JP Morgan Chase (#4) by 3%, while Microsoft and Johnson and Johnson are nearly flat, to round out the significant changes in the top 5 weighted stocks in the S&P 500. Exxon's increase alone could move the index a lot, but not as much as it has moved thanks to the other stocks. Something else is going on....

What Else Is Going On?

Not mentioned in Goldstein's reporting are two huge developments - one that has an expiration date and one that doesn't. Let's get to the one that doesn't first....

Yesterday, very big news came out from JP Morgan Chase, as CFO Mike Cavanagh announced that the bank would likely increase its dividend in 2010:

JPMorgan Chase & Co. (JPM) may increase its dividend next year and stop adding to reserves sooner, if the economy continues to recover, Chief Financial Officer Mike Cavanagh said Tuesday.

"We're going to be looking for evidence we're not double-dipping," Cavanagh said during a presentation to analysts and investors in New York. Such evidence will include "unemployment peaking and coming down" and net charge-offs on loans falling, he added.

Once that happens, JPMorgan will likely make a "significant step in the dividend in one shot," lifting the annual payout to between 75 cents and $1 a share, from the current 20 cents a share, Cavanagh explained.

That could happen as soon as early 2010, depending on the economy, he said.

Wall Street sign (Source: FBI) Factoring in the market's weighting of JP Morgan Chase in the S&P 500, this news lifted the expected future growth rate of dividends per share for the entire index by 1.7 cents per quarter. We believe that change, combined with speculation that other financial institutions that have been in the TARP doghouse for the past year may soon follow suit is likely responsible for a good portion of the stock market's rise today, which we can confirm by observing that the financial stocks of the DJI are all up more than 2% today. /p>

But not all. Even with this change in the expected future growth rate of the S&P 500's dividends per share, we find that stock prices would, at most, average somewhere between a level of 1005 at the low end (based on an amplification factor of 6.5 in our method of projecting the value of stocks) and 1037 at the upper end (based on an amplification factor of 11.0.) These amplification factors correspond to our observations of the U.S. stock market since January 2001.

Money Off the Sidelines

Our working theory is that stock prices are being boosted by additional money is coming off the metaphorical sidelines. Not from investors who haven't been investing, but rather from major traders who fled the stock market a year ago and parked the money that they took out in U.S. Treasuries.

Recession Probability vs Time: 26 April 2009 through 26 March 2010This gets to our longstanding prediction that we would see an eruption of noise in the stock market somewhere between 10 September 2009 through 16 September 2009, which we observed in the form of a sudden reversal of a falling trend in the future probability of a U.S. recession.

Since our preferred recession prediction model incorporates data related to the U.S. Federal Reserve's Federal Funds Rate and the spread between 10-Year and 3-Month U.S. Constant Maturity Treasuries, most of the changes we've observed in seeing a sudden reversal of the resulting recession probability were correlated with a sudden narrowing of the U.S. Treasury yield spread.

We believe that these events were, after a year's time, reflected in the U.S. stock market by suddenly declining stock prices. Here, we believe that bond market traders used stock options and stock purchases as part of a hedging strategy against the potential inflation risk implied by the flattening of the U.S. Treasury yield curve. After a year's time, as the options contracts and bond redemption holding period restrictions expired, this hedging strategy results in a larger than average number of shares coming in to be sold in the stock market.

Federal Funds Rate and 10 Year-3 Month U.S. Treasury Yield Spread, 2 June 2008 to 29 December 2008 That was the thinking behind our original prediction for where stock prices would go in September 2009. But as we found in digging deeper into the data surrounding the recession probability uptick we observed that would apply for 10 September 2009 through 16 September 2009, something very different happened, which led us to reverse our predicted outcome, as we signaled in our update to that post on 10 September 2009.

Instead of being the result of a sudden flattening or inverting of the U.S. Treasury yield curve, this period was defined by a dramatic widening of the U.S. Treasury yield spread. And with it clear that the flow of money effectively being reversed, we anticipated that stocks would rise substantially during this period, as a good portion of the substantial amount of money taken out of stocks and stashed in one-year U.S. Treasuries for safekeeping during the fiscal crisis of September 2008 is now free to reenter the stock market.

From our perspective, it's still a noise-driven event, which will have an expiration date. With prices having risen well above the range that their fundamental drivers of value would place them, we consider it to be a selling opportunity.

Update 17 September 2009: Barry Ritholtz posts commentary by James Bianco that suggests that we're very much on the right track with our analysis.

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September 15, 2009

We couldn't help notice an unusual coincidence yesterday. First, the Economic Freedom of the World 2009 Annual Report has just been released by the Fraser Institute (HT: DoL), which is itself a pretty momentous event. Then we found that Will Franklin has tapped the Fraser Institute's 2008 Economic Freedom of North America to create a chart that ranks individual U.S. states and Canadian provinces according to their relative levels of economic freedom.

We thought we'd mark the occasion by taking the figures we already had for each U.S. state and Canadian province's GDP per Capita adjusted for Purchasing Power Parity for 2004 and correlate that data with their respective Economic Freedom Index score from 2008. The chart below reveals what we found:

GDP-PPP per Capita 2004 vs Economic Freedom Index Score 2008, U.S. and Canada

It would appear that there's a pretty strong correlation between how much economic output a state or province generates per person and the level of economic freedom that exists in each.

Will Franklin comments on the Economic Freedom Index and the general correlation he observes between it and how a state or province performs economically:

The index is based on 10 components in three categories:

1) Size of Government;
2) Takings and Discriminatory Taxation; and
3) Labour Market Freedom.

Interesting is how many of the most free states and provinces in the study are performing better economically than the states and provinces in the bottom half of the study.

Indeed.

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September 14, 2009

Taxpayer Cash for Clunkers! By most objective measures of its environmental and economic benefits, the Obama's administration's "Cash for Clunkers" program has been a bust. But through all the discussion and debate around the program, it has gone largely unquestioned that the government-subsidized trade in of some 690,114 gas guzzling vehicles in favor of much more fuel efficient vehicles would result in less gasoline being consumed United States.

Until today. Will the Cash for Clunkers program actually reduce the amount of gasoline consumed by Americans?

To find out, we first had to establish a baseline for comparison. To do that, we need to identify the basic characteristics of both the typical "clunker" being traded in and the characteristics of the typical brand new replacement vehicle. Here, we found that the typical "clunker" is an 13 year old SUV that gets an average mileage of 16 MPG as is being traded in with an odometer reading of 138,000 miles. The typical replacement vehicle however is a brand new automobile that gets an average miles of 27 MPG.

At first glance, it would seem that the typical new vehicle replacement would indeed consume much fewer gallons of gasoline than the typical clunker. But that assumes that the new vehicle would be driven the same number of miles per year going forward as the clunker was being driven in the years before it was traded in. Is that a realistic assumption?

Average Annual Miles per Vehicle by Vehicle Type and Age, May 4, 1999, Source: U.S. Dept. of Energy To answer that question, we next needed to find out how far the typical brand new vehicle replacing the typical old clunker would be driven. We found that basic bit of data posted as the U.S. Department of Energy's Fact of the Week #87, which provided the average annual number of miles by vehicle, by vehicle type and age.

What this data indicates is that a brand new automobile in the U.S. would reasonably be expected to be driven 14,319 miles per year, at least for its first five years on the road. That contrasts with the 10,985 miles per year that the average 10-15 year old SUV was driven in 1999. As a result, it would appear that the new vehicle would be driven 3,334 miles more per year.

And that's when we noticed that something wasn't quite adding up right in the numbers we were seeing. The Department of Energy's numbers for 1999 clearly indicate that an average SUV would be driven 15,350 miles per year for its first five years on the road, 13,979 miles per year for its sixth through tenth years on the road, and 10,985 miles per year for years 11 through 15.

Average Distance Driven by Vehicle Age That would mean that the typical SUV in 1999 would have accumulated some 179,600 miles on its odometer by the time it had reached the age of 13 years old, the same average age of the typical clunker traded in as part of the government's Cash for Clunkers program in 2009.

But the average odometer reading for a 13 year old clunker in 2009 was 138,400, a discrepancy of 41,600 miles!

That discrepancy confirms that the average 13-year old clunker in 2009 was being driven a lot less than its 1999 counterpart. But why?

Given the improvements in the quality of automotive manufacturing and repair service over time, it didn't make sense that the 13-year old SUV originally produced in 1996 (to become a clunker in 2009) would be driven so much less than an SUV originally produced in 1986. Something else has to account for the discrepancy.

Average U.S. Price per Gallon of Unleaded Gasoline, Including Taxes, Adjusted for Inflation Something that would explain that however is the change in fuel prices over time. We know, for instance, that gasoline prices today are substantially higher than they were ten years ago, so the much higher cost of operating vehicles today could explain they're being driven much less.

We found that for the 13 years from 1986 to 1999, the price of unleaded gasoline in the U.S. including taxes and adjusted for inflation averaged $1.69 per gallon in constant 2008 U.S. dollars. Meanwhile, between the 13 years from 1996 and 2009, the price of gasoline averaged an inflation-adjusted $2.09 per gallon, a 23.6% increase.

But that's not all. We also found that for the first eight years of driving for 13-year old vehicles in 1999 and 2009, the average price of gasoline was nearly equivalent, at $1.76 for the vehicle hitting the road in 1986 and at $1.73 for the vehicle hitting the road in 1996.

Average Distance Driven by Vehicle Age, with 2009 Clunker Trajectory What that suggests to us is that vehicles being first driven in 1986 and 1996 would have nearly identical odometer readings through their first eight years on the road. The discrepancy would have to primarily occur after the eighth year of driving!

What we found when we factored that into our calculations is that the 13-year old clunker would only be driven an average distance of just 3,863 miles per year.

If we assume that the typical new vehicle replacement then is being driven the same average distance as its 1999 counterpart, that indicates that the vehicle will be driven some 10,456 miles further than the vehicle it is replacing. Dividing the miles driven by the clunker and the new vehicle by their respective mileage figures, we find that the clunker would consume 241 gallons of gas in a year over which it would be driven 3,863 miles, while its new replacement will burn 530 gallons of gas over the 14,319 miles it will be driven.

Average Annual Miles Driven, 13 Year Old Clunker vs New Automobile, 2009 Average Annual Gasoline Consumed, 13 Year Old Clunker vs New Automobile, 2009

We therefore find that taking the average clunker off the road will result in an additional 289 gallons of gasoline being consumed by its typical replacement, above and beyond what the clunker itself would consume if it had been left on the road!

Needless to say, we also find that the Cash for Clunkers program to be a bigger bust than was believed before.

 

 

Update 15 September 2009: Gavin Andresen e-mails a very good point (from Australia?!):

... I think your analysis of cash for clunkers is wrong.

I suspect that many of the clunkers that were traded in were "second" cars -- driven rarely because their owners have a newer, better "first" car.

The new cars from the cash-for-clunkers program WILL get driven more... but that should be offset because now the old "first car" is the "second car", and will be driven less.

I may be wrong, but my guess (and it's only a guess) is that cash-for-clunkers won't have a statistically significant effect on overall gasoline usage one way or another.

We believe that Gavin is almost absolutely correct (we say "almost absolutely" since there will likely be a small number of single car households that participated in the program.)

Going to Gavin's main point, we agree that the majority of program's transactions came from multiple car-owning households and that the cumulative distance driven for each former clunker-owning household will likely be balanced across several vehicles, as the actual miles driven would be shared among the more fuel efficient cars they own: the new "clunker-replacement" and whatever other vehicles they were already driving in place of their clunker. We also think that in terms of the aggregate statistics, any change in overall gas consumption due to the program for the U.S. will be unnoticeable as it will likely be indistinguishable from noise in the data.

However, as long as politicians continue to champion "reduced gas consumption" or "increased energy independence" as an achievement of the program or a reason to repeat it, we reserve the right to point to our direct clunker-to-new-car replacement analysis!...

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September 11, 2009

Carnival Midway from The Jerk Welcome to the Friday, September 11, 2009 edition of On the Moneyed Midways! Each week, we seek out the best posts from the past week's business and money-related blog carnivals and present them here to kick off your weekend reading entertainment!

But that's not all! For those of you who aren't satisfied with a list of the best posts we found in the week that was, we've gone the extra mile to identify the posts that are Absolutely essential reading, our signal to you of the posts that rank among the best of the year. And for the truly time-constrained, who can only devote enough time to read just one money-or-business-related blog post, we've awarded the one post you need to read with the title of being The Best Post of the Week, Anywhere!.

And for the very truly time constrained, we'll stop going on and let you get right to it....

On the Moneyed Midways for September 11, 2009
Carnival Post Blog Comments
Carnival of Debt Reduction What Happens When You Run Out of People to Blame? Financial Methods Trisha Tolar finds that the number one obstacle preventing you from being happy, successful or debt-free is very likely looking right back at you in the mirror.
Carnival of Personal Finance Where to Find Other Sources of Income Canadian Finance Tom notes the two ways people can improve their personal finance situation: cutting their spending and increasing their income. Here, he considers a number of options for bringing more money home.
Carnival of Taxes The Next Bubble: Your Taxes Don't Quit Your Day Job Paul Kamp sees higher taxes in America's future, and argues in favor of taking advantage of a law that will remove the limits on how much money can be transferred from a taxable Traditional IRA into a non-taxable Roth IRA for 2010 only.
Carnival of Taxes Cash for Appliances Is Coming - Hold Off on That Purchase! Darwin's Finance The next major "stimulus" package is already in the works for this fall! Darwin makes a compelling argument in favor of holding off on making any major appliance purchases today until the government's "Cash for Clunker Appliances" program is up and running. Darwin's post is The Best Post of the Week, Anywhere!
Cavalcade of Risk Money Transfer in Kenya Evolves Bankelele Bankelele delivers Absolutely essential reading with a post that considers how "mobile money," or rather, payments made via cell phone accounts technology, is taking the place of money in Kenya. The future of money could very well be being made right now in Africa!
Festival of Frugality Six Thrifty Uses for a Lemon Miss Thrifty Miss Thrifty lists six things you can use lemons for to save money. We freely admit that we never considered using lemons as a deoderant, nor as a copper cleaning agent.
Carnival of Money Stories Why Join a Credit Union? Why I'm No Longer a Traditional Bank Customer The Smarter Wallet Tim Parker stopped using banks several years ago and is surprised that anyone does today. Here, he explains why.
Carnival of Pecuniary Delights Cleaning Silver - This One's a Beauty Miss Thrifty After having selected her post on using lemons to accomplish a number of household tasks, we couldn't pass up Miss Thrifty's ingenious use of hot water, salt and aluminum foil to clean silver. Who knew?

Previous Editions

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September 10, 2009

The winning design of the James Dyson Award for 2009 has been announced, and we're not kidding when we say that it's one of the neatest design concepts we've seen that also has exceptional practical value. Meet the Automist, a device that transforms the common kitchen sink into an extremely effective home fire suppression system (HT: Core77):

Illustration of the Automist at Work

Let's take you through each of the panels in the illustration above:

  1. The Automist is installed at the base of the faucet in a kitchen sink.

  2. A fire breaks out in the kitchen.

  3. Smoke sets off the kitchen smoke alarm.

  4. The smoke alarm sends a signal to the Automist water control valve.

  5. The valve opens, sending a torrent of cool water-mist from the base of the sink's faucet in all directions.

  6. The water-mist acts to suppress both the fire and its spread, protecting the home from significant fire damage.

Better still, here's the YouTube video for the contest entry:

The potential of the invention for reducing losses related to home fires is pretty remarkable. For their efforts, the contest winners Yusuf Muhammad and Paul Thomas of the Royal College of Art have won £10,000 to help develop their design further toward entry into the market.

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September 9, 2009

Ultra-Concentrated Downy Fabric Softener, 34 fl. oz., Source: Amazon.com When it comes to buying stuff that comes in different size packages, it often makes more sense to buy a particular item in a bigger package than in a smaller one.

The reason why comes down to that item's unit price for its different sized packages - how much it costs for a given standard quantity. For example, we could buy a 34 fluid ounce package of ultra-concentrated Downy fabric softener for $7.83 from Amazon, which works out to be $0.23 per fluid ounce.

Or we could buy a 6-pack of the same bottles of fabric softener from Amazon for $36.76, which drops the unit price for the exact same item down to $0.18 per fluid ounce, making it a potentially better deal.

We say "potentially better" because there are other things that might make the same item in a smaller size more desirable. For instance, we might not have adequate storage space for a 6-pack of 34 fl. oz. containers (204 fluid ounces in all), which would make having more than one a real inconvenience. Or in the case of perishable goods, like those ginormous containers of mayonnaise that you see at warehouse club stores, the contents of a bigger container might spoil before we can use it all, which would mean that our money would go to waste as well.

And speaking of money, we may have some budgetary issues in that we might have $7.86 available to buy the smaller container, but not $36.76 to buy the greater quantity. That's not so much to say that we don't have $36.76, but more to say that we'd rather spend the difference on something other than making our fabrics softer.

Coupon Clipping All that however is small potatoes compared to the potential unit price distorting power of coupons! Here, thanks to those glossy paper inserts you're most likely to find in the Sunday edition of your local newspaper, the discount you might get on a smaller item might more than make up for the discount you might get by buying bulk quantities!

We'll test that idea in the tool below. Here, we'll plug in our Downy default data, then consider what happens when we have a coupon that provides a $1.00 savings per package, such as we might find on the Downy promotions web site. Would it still be more economical to buy the greater quantity? We'll answer below the tool, which can easily be altered to consider whatever product cost and quantity comparison you might actually want to do....

Product Price and Quantity Data
Input Data Item Price Unit Quantity
Smaller Package
Larger Package
Coupon Discount Data
Amount of Coupon Discount per Package


Which Size Is the Better Deal?
Calculated Results Values
Smaller Package Unit Price
Larger Package Unit Price
The Bottom Line

For our fabric softener example, with the $1.00 off coupon, we find that the 6-pack is still the better buy, as it saves 2.6 cents per fluid ounce over buying the single 34 fluid ounce container. But without the coupon, the 6-pack is an even better buy, saving 5.0 cents per fluid ounce over buying the single container.

Having closed the gap by that much, we wondered what kind of coupon discount it would take to make the smaller container have the better unit price. Playing with the tool, we found that a discount of $2.05 marked the point where the smaller package would have a slightly lower unit price. More than that amount and it would be the better deal.

While that's an unlikely amount to find printed on a coupon, you might get pretty close to that number if the store where you might buy the item you're purchasing is one that doubles or triples the face value of coupons as part of a sales promotion.

It's no wonder that so many different coupon services have taken off in recent years!

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