Additional Math Pages & Resources

Tuesday, November 29, 2011

Counting Up to 180, Part I

Yesterday I complained about subtraction from my paycheck. Today I am celebrating an addition to my Flag Count. I can now count up to 180 - and I have learned to do this while writing this blog about elementary math.

If you can't recall, counting up and down are part of the math curriculum in elementary school. In Excel Math, kids get to a hundred in Kindergarten, and way past 100 when in First Grade. Here's the first part of the Counting past 100 lesson:

It turns out that in addition to counting, you can learn an awful lot about world geography while doing a blog. During the past 2.5 years and 550 posts, at least 75,000 different people from 180 countries have stopped by for a look.

Today I'm going to give you a chance to find your own place on that list. Here are the top 10 countries, in descending order by country and state (province/region). I get these figures from a handy resource called Flag Counter:

NOTE: "51 of 51 collected" or similar numbers, means state and national flags for that country. There are 51 in the USA, counting all the states and the national flag. Wonder where the territories are? We'll take a look for them tomorrow.

This may look like the easiest post I've ever written for this blog, but it took quite awhile for me to decide on the best way to present this data. That's often the case with math - you do the calculations quite quickly, but then have to determine which data is essential, which can be edited or streamlined, and which might work against you and ought to be omitted. 

We'll have lots more visitor information tomorrow, including those US territories I mentioned earlier.

Subtraction Is NOT My Favorite Operation

Operation is a word with multiple meanings. It implies that a surgeon is going to cut away at you, or in the math world, it means making changes to a set of numbers or other sorts of manipulation of math objects.

More technically, we could say, an operation is taking one or more input values and combining them in different ways. These combinations include addition, subtraction, multiplication, division, and exponentiation. You can combine logical statements as well as numbers, such as IF A happens, THEN B happens too, or IF C is TRUE, then D is FALSE.

In this case I am complaining about SUBTRACTION. Why?

It's the time of year when those of us fortunate enough to have jobs look forward to our year-end paychecks. We start to worry about owing "the man"  (Federal and State) more money than we have had withheld. We think about contributions we might make to churches or charities.

We might even have to subtract extra amounts from our paychecks to cover our exposure!

Here are the potential additions on our paychecks:
Base Salary (Rate x Hours)
Pro Rata or Overtime
Workers Comp Pay
Vacation Time
Family Leave or Bereavement

Here are the actual subtractions!
401k withholding
Medical Reimbursement / Cafeteria Plan
Medical Insurance
Life Insurance
Federal Income Tax
Federal Medicare
Federal Social Security
California Income Tax
California Disability
Employee Association Dues
Community Association Donation

Take a look at your own pay stub to see all the things that come out.

Now I know that these are not all taxes, and I am not complaining about the rate of tax I am paying. Some of the deductions even reduce our taxable income, thus saving money.

But when the NET amount on this particular paycheck is less than 26% of the GROSS amount, I get mad at the math operation known as subtraction!

But my anger dissipated when I found this distracting sentence on my wife's employer website:

Our school district takes out payroll deductions on a tenthly basis. Any tax required to be paid on a twelfthly basis is "caught up" on the October payroll each year.

Try saying twelfthly a few times! Seven consonants, two vowels. Too much tongue!

Monday, November 28, 2011

Statistics is a Contact Sport

" All we want are the facts, ma'am. "

This quote came from Detective Sargeant Joe Friday, of Dragnet radio and television fame. It could safely be said about math too, as people (unwisely) think math is all about facts.

But math is not all facts. This was brought to my mind this morning while I was reading about an investigation of financial statistics in Greece.

Statistics does involves numbers and math but is far from being a "factual" business. As I look at our statistics lessons in the Excel Math curriculum, I'm not sure we adequately prepare kids for deliberate manipulation of the numbers that can occur with statistics. We start to teach it in Fifth grade.

"Sir, It has been wittily remarked that there are three kinds of falsehood: the first is a 'fib,' the second is a downright lie, and the third and most aggravated is statistics. It is on statistics and on the absence of statistics that the advocate of national pensions relies ..." 

We don't know who first said this, but it's popularly associated with Mark Twain. He in turn claimed it was first spoken by Benjamin Disraeli.

Reading further on the issue of Greek financial turmoil, I was impressed with these assertions:

1. Accounting numbers are soft because they depend on assumptions and conventions; government accounting is even softer for many reasons

2. Governments may deliberately inflate inherited budget deficits by shifting discretionary items around to
    (a) score points against the party that was previously in power, and
    (b) prepare the ground for retracting pre-election promises.

3. Debt incurred by Greece is described as a percentage (15.8%) of the country's earned income. That income figure is constructed based on the taxes collected by the government. Since an additional 30-50% or more of Greek national income may be "black market" (evades taxation), the percentage of debt compared to the "real" total income could be much lower ...
4. This is not new. Statistics have always been used to manipulate numbers and to ensure that pre-determined policy decisions are later viewed in the most advantageous way.

The Greek statistics bureau chief was quoted in the article as saying,

"We would like to be a good, boring institution doing its job. Unfortunately, in Greece, statistics is a combat sport."

We in the US would say "contact sport."

Recent Google news items have described Thanksgiving Weekend Mall Shopping, Climate Science, Investing and cross-country running as "contact sports".

So why not statistics?!

Wednesday, November 23, 2011

Using Elementary Math When We Grow Old, Part II

The subtitle of this blog is normally using elementary math when we grow up. This week it's using elementary math when we grow old. We're talking retirement. Ouch!

Yesterday I provided some obscure formulas that were truly intended to model the growth and shrinkage of retirement funds, and suggested that most retirement decisions were not math-based.

Why retire?
Here are some reasons people give for retiring at the age that they did; only a few involve money:
  • I am in poor health and can't perform my job well, or I no longer enjoy my job
  • I have lots of 
    • outside interests and hobbies
    • charitable work to do
  • I want to move to a new place (city, state, country)
    • lower taxes
    • better weather
    • more family and friends
  • I want to use up my children's inheritance savings
Why not retire?
Here are a few reasons that I've found; not all are math-related:
  • too many bills right now (house, car, kids, credit cards)
  • not enough income or savings for future expenses
  • fear of losing friendships at work
  • fear of dying after stopping work
  • fear of boredom and stereotypical senior activities
What will I do if I retire?
Will I be walking in the mall with a bunch of other folks?

Will I be sitting out on a tropical beach while my hair goes white (if I have any left)?

Will I gather with my fellow seniors on our recumbent tricycles and terrorize our trailer park retirement village?

Or will I be working as a greeter in a discount store?

Notice these are not necessarily financial issues. However, it's true that retirement raises many financial questions. The primary one seems to be:

Will I outlive my money?

At the moment, our country is in debt and we can't continue to pay all the pensions, Social Security and Medicare benefits we once thought we could afford. Some of us won't have as much retirement wealth as we had hoped, because the markets are depressed. So we have more questions:

Where do I live? In what things do I invest? How much do I save? When do I withdraw my money and how much? How can I minimize my taxes?

If I had those answers I would not be writing elementary math curriculum!

The simplest response is to say "Watch your spending, watch your income and balance them. Spend less than you have coming in." That's probably not the best approach for the economy at large, but in my opinion it's the best strategy for a household.

When you look at the big picture, even having the opportunity to consider retiring before we die is an indication that many of us are living in a stable country, above a subsistence level. And for that we can be very grateful.

Have a nice Thanksgiving.

Tuesday, November 22, 2011

Using Elementary Math When We Grow Old. Part I

For two years, the subtitle of this blog has been "using elementary math when we grow up." Today I am making a temporary adjustment to " using elementary math when we grow old ."

Life includes these activities - we are born, we grow up, we get an education, we work, we retire, and we die.  Normally I deal with education or work, but today I want to consider retirement.

I suggest a quick trip to the Wikipedia page on retirement for an overview of this topic.  

Retirement means stopping work and paying for things with our savings or a pension earned during our working life (or we may depend on our families, or the government). In the stereotypical American Dream, it means golf, and bridge, and cruises, and walks on the beach ...
Why do beaches and bicycles always appear in retirement planning brochures?

Germany was the first to introduce retirement in the 1880s, about the same time that the USA introduced state-mandated, universal education. Since then, most countries have adopted both mandatory education for youth, and government-encouraged or government-mandated retirement for seniors.

Are Retirement and Education related to Unemployment?
Perhaps there is no direct cause-effect relationship, but consider this - because many governments insist on both
  1. childhood education (which delays our entrance into the workforce) and 
  2. senior retirement (which speeds our departure from the workforce)
in most developed countries, there are a few more working hours at either end of our lives, now available for others to fill. That might reduce unemployment for a few, while the retired among us can work on their hobbies instead of a job - like my old Polish friend in Paris, restoring his car...

Is Retirement Advisable? or Desirable? or Inevitable?
Not necessarily.

If people earn and save a lot when they are working hard, will they retire as soon as they have enough money? No. They won't. Look it up if you like, the evidence is clear.

Can Math Help?
Yes, but it's not simple math. Not elementary math. See the formula below on calculating savings during your working years. If you can figure it out, and have saved as it suggests, you are probably smart enough to retire today:

Decisions to retire seem to be based on a combination of wealth, health, family and interests. Money is only a part of it, although no one wants to run out of money before they die, of course.

See the formula below on calculating spending down your retirement savings by age 120. If it doesn't make sense to you, maybe you are not yet ready to retire!

You can talk to your investment advisor, or talk with your spouse, or sign up for a night class in retirement math - they might be able to shine a light on your retirement future.

Tomorrow we'll tackle the math part of retirement from another angle.

Monday, November 21, 2011

Simple Math Samples

Although many people consider elementary math to be "simple math," parents who have to explain it to their kids may disagree. Our math might be elementary, but it's not simple. In an effort to understand what things about math could be considered simple vs complex, I did a little research today.

As I searched for the terms "simple" and "math," I noticed the results didn't have any direct relationship to the math we cover in our elementary schools. Nor did they discuss what makes math simple or hard. I did however find some interesting material. Here are a few sites I found:

Simple Math Cellars - a winery in northern California. The idea of Simple Math Wine is not about what’s on the tech sheet but what’s in the glass - yum? or yuck?

Simple Math - an alternative, conceptual, grunge, indie-pop music album by a group called Manchester Orchestra, released in May 2011.

Simple -  a site selling an Apple iPhone app that generates practice math problems for kids.

Retail Math Made Simple
- a virtual site that sells a book full of math to retail store managers. It covers things like inventory, discounts and pricing, ordering lag times, etc.

Simple Math Bakery - a blog focused on a lady's baking experiences - there seem to be all sorts of nice things whose ingredients are easy to calculate.

Simple Math Guild - a group of computer gamers who quite frankly I don't understand and can't explain, so read it in their own words:
In 2005 on the oceanic server of Frostmourne, members of the guilds Gun It and Throat Stab merged into a guild called Dark Matter. After a short time of raiding there were some leadership issues and about 20 people left to form a new guild. The name Simple Math was derived from a guild joke regarding the aggro transfer for tanks during the Kurinnaxx fight in AQ20. Shortly after arriving on the Andorhal server we found  new members and soon we had killed Ragnaros, Neferian, and Fandral Staghelm. At this point we halted raiding until the release of Burning Crusade. The Simple Math of Burning Crusade started with a massive struggle for power and continued once we got our ranks in order. We came out in first place on Andorhal as our competition disbanded or transferred after Lady Vashj and Kael’thas Sunstrider kills. No turning back now!

Simple Math Fairy Tales - a series of graphics using math formulas to present Fairy Tales - done this year in an advertising campaign for a Canadian Toy Store. For example:

Simple Math - a blog posting that tries to explain why fees for creative agencies are rising very quickly relative to the marketing campaigns they create or manage:
We hear "Agency fees have been growing faster than our digital media spending. Something is wrong and it has to stop!" The reality:  Nothing is wrong. Clients are spending more on Owned media - the things we build such as applications, web experiences, etc.  There’s no media (magazine, newspaper) cost - only agency fees for building these things.  Earned media is what customers are saying to each other - social experiences that are being built, monitored, and managed. Again, no media cost, only fees for what we do. The better we get at exploiting the power of owned and earned media, the faster agency fees will rise relative to media costs. If a $500k marketing program (all fees) performs as well as a $10-million paid media program (10% fees + 90% media), who really is hurting?  Answer: the media publishers, not the client. Not us.

Simple Math of Everything
- a proposed book, to contain specialty math knowledge from every field, without going beyond introductory level:
There's a substantial advantage in knowing the drop-dead basic fundamental embarrassingly-simple mathematics in as many different subjects as you can manage. Not the high-falutin' complicated math that appears in the latest journal articles (unless you plan to become a professional in the field). For people who can read calculus, and just plain algebra, the basic mathematics of a field may not take long to learn, and is likely to change your outlook on life more than either math-free popularizations of that subject, OR its highly technical math.

In my estimation, this book is not likely to be written, as no single person has the time or energy or breadth of knowledge to write it on his/her own, and writing by committee is even harder and takes much longer (been there, done that).

Simple Excel Math - Here's what we teach in the first few months of Kindergarten. Is this simple?
  • Recognizing/using position words: top, bottom, over, under, above and below
  • Recognizing/using time words: morning, afternoon, evening and night; days of the week 
  • Recognizing/using position words: left, right, between and middle 
  • Recognizing/using left and right hands; moving from left to right 
  • Identifying which of 3 items is different from others in the set 
  • Recognizing the shape of numerals 0, 1, 2, 3
  • Recognizing/using position words: inside and outside, on and off 
  • Recognizing/using position (in time) words: before and after 
  • Learning the concept of 1 and 2 
  • Recognizing left and right and moving in those directions when asked 
  • Learning the concept of 3
  • Recognizing the shape of numerals 0, 1, 2, 3, 4, 5
  • Recognizing measurement words: taller, shorter and same height 
  • Copying a pattern of shapes 
  • Copying a pattern of hand motions using cards with 2 colors and letters 
  • Identifying which of 3 items is unique
  • Learning the concept of 4
  • Counting and showing numbers 0-5 with fingers
  • Circling 1 to 4 items in a set 
  • Counting objects in a set; sorting shapes based on similar characteristics 
  • Repeating a pattern of postures or body movements 
  • Comparing pairs of lines of different lengths 
  • Learning the concept of 5

Friday, November 4, 2011

Recommended Daily Allowances

Contrary to what you might think, this post is not about the money you should give your kids - it's about the ideal selection of food and drink we should consume each day.

Math you learned in elementary school (hopefully using our Excel Math curriculum) should be adequate for you to monitor your own nutritional intake.

RDA is part of a larger scheme called the Dietary Reference Intake. The Dietary Reference Intake recommendations for US and Canadian citizens include:
  • Estimated Average Requirements (EAR) - the amount of food that should satisfy 50% of the people in a specific age or gender group. EAR is determined by a committee reviewing recent scientific literature.

  • Recommended Dietary Allowances (RDA) - the daily quantity of a substance which the Food and Nutrition Board feels will meet the needs of virtually all (97–98%) healthy individuals. It is approximately 20% higher than the EAR.

  • Adequate Intake (AI) - used where no RDA has been established. This amount is felt to be barely adequate for everyone in a demographic group.

  • Tolerable Upper Intake Levels (UL) or Acceptable Daily Intake (ADI) - these are ceiling levels, to prevent excessive intake of nutrients (like vitamin A or D) that can be toxic. This is the highest level of daily consumption that is unlikely to cause side effects when taken long term, without medical supervision.
These recommendations, even on the healthiest of foods, are subject to intense debate, discussion and disagreement among health and nutrition professionals!

NOTE: The DRI levels cover only what we feed ourselves. Other substances ingested due to packaging, contamination, pesticides, spoilage, etc. are measured in terms of cumulative contact or consumption over a long period of time.

In the case of Vitamin D, yesterday's topic, we each have a different ability to synthesize it from the sun exposure and diet. We live in varying places on the globe, have differing amounts of clothing on when we go outdoors, have unique skin coloration and blocking abilities, etc.

Even in Sunny Southern California, many people have low vitamin D levels because we have become very careful about sun exposure (causing skin cancer), and we don't drink as much milk as we used to (fortified with vitamin D). In theory, the RDA of 600 IUs of vitamin D should be adequate to maintain bone health and calcium metabolism, but due to low levels in many people in the USA, there is ongoing debate about raising the RDA.

Although sunlight is a major source of vitamin D for some, the vitamin D RDAs assume minimal sun exposure. If you want to enhance your own Vitamin D levels through sunshine, be aware that cloud cover reduces UV energy by 50% and shade reduces it by 60%. Window glass and sunscreens of SPF 8 or higher block all vitamin D production.

As described yesterday, it's possible to buy supplements to assist your body with its normal intake or production of vitamin D. So now we know that we can obtain vitamin D through diet, sun or supplements, but how do we know if we have been making or taking enough?

At the moment, the only way to find out is through a blood test. A doctor can order the test or you can get mail-order test kits for about $50-60. Here are current recommendations from the National Institutes of Heath; the numbers represent nanograms per milliliter of 25-hydroxyvitamin D:

 D Level  Health Status & Consequences
< 30 Deficiency, leading to rickets and osteomalacia; possible connections to heart disease, asthma or cancer
30–50 May be inadequate for bone and overall health in healthy individuals
50–80 Considered adequate for bone and overall health in healthy individuals
> 125 Possible that there may be adverse effects from levels this high

My tests said I had a level of 12-15. That's far too low, so I was prescribed Vitamin D supplements. After 50,000 IUs per week for 3 months to catch up, my doctor told me to take 1000–2000 IUs per day and get outdoors more often. A follow-up test shows my vitamin D level is approaching 50.

My health care provider told me that one-third of Americans have low vitamin D levels, and many people are being asked to improve their diet and sun exposure or take supplements. Your doctor might have the same advice for you, and now you know the math you need to monitor yourself.

PS - I am taking a week or so off this blog so I can go outside and get my Vitamin D levels up ... and read through Wikipedia's Vitamin D page.

Thursday, November 3, 2011

Comparison Pricing for International Units

Today's blog is concerned with comparison price shopping for vitamins. I have compared prices before, about two years ago when pricing a cup of tea, and last summer in showing how our Excel Math curriculum helps kids learn to compare item pricing. This post is a bit more complex.

I have been taking vitamin D (ordered by my regular doctor) because I can't spend too much time in the sun (according to my skin doctor). Most of us get vitamin D from food sources and from sunlight. A few people, in some sunny areas, get adequate amounts of vitamin D directly from the sun, via UV rays which trigger vitamin D synthesis in their skin. The great majority of us who lead indoor lives need more D than we get from sun exposure.

I have learned that buying vitamins is a bit like shopping for a mobile phone plan, or buying a new mattress. In other words, complicated!

Vitamins are "measured" in International Units. This measuring system has nothing to do with the International System of Units (what we Americans tend to call "metric"). Bear with me while I explain this:

What is an International Unit?
An IU is a unit of measure describing the quantity of a substance that achieves a certain amount of biological activity in the body. It is used with vitamins, hormones, medications, and other biologically-active materials. Different biological preparations may have the same effect in the body; the purpose of the IU is to be able to compare them. Any formulation with the same biological effect (regardless of weight or volume) contains the same number of IUs. 

How do we determine an IU and who does this?
The World Heath Organization has a special committee that prepares a reference compound (mixture) of a biological material and arbitrarily determines the number of IUs contained in it. They also specify the laboratory procedure used to compare other formulations with equal effect as the reference compound.

Thanks to this process, one IU of vitamin E is the same as any other IU of Vitamin E. However, there is no equivalence or direct comparison between IUs of Vitamin E with those of vitamin A or D, or insulin or penicillin.

In the case of Vitamin D, one IU is the biological equivalent of a very small amount (2.5 percent of a microgram, or 0.025 μg) of D3 cholecalciferol or D2 ergocalciferol. Our bodies need a lot more than 1 IU per day - more like hundreds of thousands of IUs.

How we decide the Recommended Daily Allowance (RDA)  and who does this?
Or to put another way, how many IUs of any substance you may need to consume each day? That is a question I cannot answer today. Do you mind if we tackle that tomorrow?

Now where were we? Oh yes, shopping.

In this case the common comparison of price per item is useless, because one pill can contain varying amounts of Vitamin D. And there are many different quantities in a bottle. You can purchase liquid, gel, chewable tablet and other forms.

I decided to create a comparison table to see how many IUs I can get for a dollar. Here's my table comparing four  brands and various quantities and strengths of dosage. The green is the best value for an IU and the red is the most expensive per IU. The red choice is 13 times more costly per IU than the green!

 Vitamin Brand/Type Int'l Units Quantity Cost $ Calculation IUs Per $1
 Nature's Bounty D3 10,000 60 19.99 (10000 x 60) ÷ 19.99 =  30,015
 Nature's Bounty D3 5000 300 15.55 (5000 x 300) ÷ 15.55 =  96,463
 Nature's Bounty D3 2000 300 14.99 (2000 x 200) ÷ 14.99 =  26,684
 Nature's Bounty D3 1000 480 16.50 (1000 x 480) ÷ 16.50 =  29,090
 Nature Made D3 5000 90 10.70 (5000 x 90) ÷ 10.70 =  42,056
 Nature Made D3 2000 220 8.90 (2000 x 220) ÷ 8.90 =  49,438
 Nature Made D3 1000 560 7.99 (1000 x 560) ÷ 7.99 =  70,087
 Nature Made D3 400 240 12.89 (400 x 240) ÷ 12.89 =  7,447
 Thorne D3 25,000 60 21.60 (25,000 x 60) ÷ 21.60 =  69,444
 Thorne D3 10,000 60 16.50 (10,000 x 60) ÷ 16.50 =  36,363
 Wellesse D3 Liquid 1000 48 6.29 (1000 x 48) ÷ 6.29 =  7,631

If you want more information, here's a place where all kinds of units are defined and compared.

Wednesday, November 2, 2011

What if for the third and final time

This week we've been investigating What If? questions, and how math comes into the picture.
  • What if I bought this house?
  • What if I took this job?
  • What if we invested in this company's stock?
Answering What If? questions can be considered gambling - "an enterprise undertaken or attempted with a risk of loss and a chance of profit or success." Even using math to carefully analyze the odds, we are still prospecting (looking for gold) in a wilderness!
In this rough economy, many of us have learned that investing resembles gambling more than it does saving.

One way to reduce mistakes in our What If? choices is to collect and consider information BEFORE choosing a course of action. We provide opportunities for elementary school kids to do this via our Excel Math curriculum. However, for adults it can be a complex challenge!

A site called "The Informed Investor's Forum" claims:

"our forums allow investors to hear directly from company executives, and to ask questions before they invest. Companies benefit by presenting their story to highly engaged, serious investors who, on average, research their investments diligently, make larger investments and hold their investments for 5 years or more." 

Is that your profile? Or do you get a tip from a friend and buy a stock?

One of my quirks is that I actually like to read the fine print in agreements. The following blue text is taken from a public company's website, abbreviated by 50% (!) and edited for clarity. Similar fine print is thrown at all US investors by all public companies, thanks to our Securities Exchange Commission.

The SEC encourages us to disclose forward-looking (future) information so investors can better understand our company's future prospects and make informed investment decisions. "Forward-looking statements" as defined by the Private Securities Litigation Reform Act of 1995 do not relate strictly to historical (past) or current (present) facts.

Forward-looking statements use words such as "anticipates," "estimates," "expects," "projects," "intends," "plans," "believes" in connection with discussions of future performance.

Our forward-looking statements are based on our management's current expectations and assumptions regarding the Company's forecasts of its future business, events, circumstances and results.

As with any projection or forecast, they are inherently susceptible to uncertainty

Our actual results may vary from those expressed or implied in our forward-looking statements. Actual results may differ materially from the forward-looking statements due to:
  • recent and future changes in technology, services, standards and formats
  • changes in consumer behavior, spending, and when, where and how things are consumed
  • changes in our plans, initiatives and strategies, and consumer acceptance of them
  • competitive pressures, including audience fragmentation and changes in technology
  • our ability to deal with economic slowdowns or other economic or market difficulties
  • shifting advertising expenditures, pressure from public interest groups, and other societal, political, technological and regulatory developments
  • piracy and our ability to protect ourselves and our intellectual property rights
  • lower than expected valuations associated with our cash flows and revenues
  • decreased liquidity in the capital markets and limits on our ability to gain funding
  • the effects of significant acquisitions, dispositions and other similar transactions
  • failure to meet earnings expectations
  • adequacy of our risk management
  • potential losses from terrorist acts, hostilities, natural disasters and pandemic viruses
  • effects of union or labor (talent) disputes
  • changes in accounting policies, tax rules and other federal laws and regulations
  • other risks and uncertainties detailed in Risk Factors (6 pgs in our Annual Report):
    • risks arising from the outcome of various litigation matters
    • loss of key management personnel or popular on-air and creative talent
    • risks relating to doing business internationally
    • personal influence exercised by our Chairman due to his ownership of preferred stock
Any forward-looking statements made by the Company speak only as of the date on which they are made. We expressly disclaim any obligation to update or alter these forward-looking statements, whether as a result of new information, subsequent events or otherwise.

All this means that you should take any Forward-Looking Information cum grano salis. You did study Latin, didn't you?

Just as you would expect your dinner to be mostly food, with just a little salt, so you should expect Forward-Looking Information to be primarily speculation, seasoned with just a few facts. Not the other way around.

So any math you do using this information has to be considered speculative rather than accurate!

Tuesday, November 1, 2011

What If again?

We are continuing today on the theme of yesterday's blog post entitled What If? The answers to What If? questions in the future are called scenarios. Or forecasts. Or prophecies. Or predictions. Math is what you use to calculate future numbers, based on current assumptions.

What if I buy this car instead of that one?  What if I take this job paid in tips as a waiter here, instead of that job with a salary over there, and take the extra earnings and buy a house?

It used to be popular to forecast your career earnings, estimate your home's appreciation, and predict that by year 20XX you would be able to move to a bigger house, put your kids through college, or retire. I can tell you from personal experience that my predictions seldom worked out the way I expected, no matter which scenario I used; no matter how "hot" the California real estate market was; no matter how sophisticated the mathematics.

For personal financial forecasting I have used a company called Financial Engines. Their software looks at your assets and works through thousands of scenarios. It comes up with some predictions and suggestions to assist you in retirement planning. Here's one report I got recently:

On most What If? scenarios, you can do the math yourself, using what you learned in elementary school. For example:

I was talking with a pal about sales commissions. If he was able to make a modest improvement to a client's future business, his company could charge a small fraction of that amount for his services. His calculations went like this:

If my client A increases his sales by $32 million and we charge 1.75% of that, and my employer keeps 75% of the fee, I would get the other 25% of the fee. How much do I get to keep?

Scenario 1 $32,000,000 x .0175 = $560,000 x .25 = $140,000

If A makes $22.5 million instead, we charge 1.5% and I get to keep 20%, how much is that?

Scenario 2 $22,500,000 x .0150 = $337,500 x .20 = $67,500

My friend liked both of those numbers (he liked the larger one better!) while I was thinking back to 1575 AD when this statement first appeared in English:

"Counte not thy chickens that unhatched be."