A Formula For Calculating The Best Usage Of Your Pantry

I've been thinking about optimizing our pantry usage lately.   We've got different items in there that are consumed at different rates, go on sale at different rates, are different sizes and cost different amounts.   I realized our pantry use isn't all that efficient.   We've got stuff that sits in there forever and is hardly used.   We've got some stuff that doesn't cost much and we don't save much by stocking up on during sales versus simply buying it at full retail as needed.   Larger items take up a lot of room and are less effective use of space versus smaller items.

Thinking about it a little I came up with the following factors that impact the effective use of our pantry :
It makes sense to buy stuff that has the biggest sale discount.     You'd rather have items that save you a lot in the pantry versus stuff that saves you little.
We should fill the pantry with smaller items so the smaller the better.  Best to squeeze as much stuff in there as possible.
The longer it takes to consume an item the worse.    This is because you have to store the replacement items in the pantry thus taking up space longer and minimizing your savings.

This leads me to derive the formula for valuing items in the pantry at :

Pantry value = savings / (size * consumption time)

Savings : is the amount you save on the item by buying it on sale or discount versus simply paying the standard cost at the grocery store.   This is based on the assumption that you go to the grocery store every week or as necessary and can readily buy items at a standard price.   If items never go on sale theres no need to store them in the pantry.   But if you find the item on sale $1 less than normal and stock up on it then you save $1 by putting the item in the pantry.

Size : is just a calculation of the cubic volume of the product in inches.  You can use any measure for volume you want really but I just chose inches.   Bigger items take more room and are thus less efficient use.

Consumption time : is how long it takes you to use that item and thus how long its going to be taking up space in the pantry.   If you rarely use an item then it will sit in the pantry longer and use up more space and this is less efficient then items that take space longer.   Would you rather save $10 by storing an item for a year or save $0.25 each week by storing and replenishing an item every week?

Lets compare two items we have in our pantry :

Item #1: Cheerios
A 20 oz. box of Cheerios is about 12" x 10" x 3.25".   Thats 390 cu. in.  I go through a box a week basically, as I eat a couple big bowls for breakfast.       I can get those for $3.40 at Boxed.com or similar price at Costco.    If I just buy them at the local grocery store the price tends to be more like ~$5 for a similar size box.   So I save about $1.50 by keeping Cheerios in the pantry.    But I only need to have 1 box on hand at any given time and on the other hand I don't want to be going to Costco or making Boxed.com orders every other week just for Cheerios.  

Item #2 : mac & cheese
Normally the mac and cheese we get is about $1.75.   Its not the cheap stuff.   But it is on sale for $1 a box every month or so.  We go through 1 box a week.   Each box is 6"x 8" x 1" for 48 cu. in.    They tend to go on sale about every 2 months.

The formula for pantry real value is =   ( Saving ) /   ( volume * consumption )

So for the Cheerios example I'm saving lest say $1.50 but I can buy them every week so sales period is 1.   The volume is 390 cu in and I go through a box in 1 week.    $1.50  / 390 *1 = 0.0038

By contrast the noodles are saving me $0.75 and their volume is just 48 cu.in. and they are consumed in a week.   So the formula is then 0.75  / 48*1 = 0.0156

The mac and cheese has a higher pantry value so if I were choosing real estate in the pantry I'd definitely want a box of mac & cheese over a box of Cheerios.    But what about a 2nd or 3rd or 4th box?

It takes me 2 weeks to consume a 2nd box.   It takes 3 weeks to consume the 3rd box and so forth.

That changes the formula to 2nd box = 0.75/48*2 = 0.0078 and 3rd box = 0.75/48*3 = 0.0052, 4th = 0.75/48*4 = 0.0039 and 5th = 0.0031.    Its not until the 5th box that storing the extra mac and cheese becomes less cost effective for the space versus storing the cheerios.

Storing 1-4 boxes of mac and cheese in the pantry is better use of the space than saving a box of Cheerios.   However saving more than 4 boxes of mac & cheese is less effective pantry use than a box of cheerios.


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Are People Shockingly Bad at Finance Math or is The Economist Wrong?

I while back I reported that People Are Shockingly Bad at Simple Finance Math   That was based on an article in The Economist titled  Teacher, leave them kids alone

I quoted that article saying how 'only half of Americans aged over 50 gave the correct answer' to a simple multiple choice question about how much your savings account balance would grow / drop after 5 years if it paid 2% a year.

The question in question:
Suppose you had $100 in a savings account that paid an interest rate of 2% a year. If you leave the money in the account, how much would you have accumulated after five years: more than $102, exactly $102, or less than $102? And would an investor who received 1% interest when inflation was 2% see his spending power rise, fall or stay the same?

Easy right?   (if you got it wrong you probably over thought or misinterpreted the question)

I was shocked that only 50% of people would get that simple question wrong.

Then recently I saw Bargaineering asking How Financially Literate are You? and they gave a quiz from the  FINRA Investor Education Foundation National Financial Capability Study
I recognized that the #1 question on that quiz is the same simple question about how savings grows over 5 years at 2% a year.

I found the full report :  Financial Capability in the United States Report of Findings from the 2012 National Financial Capability Study

If you go to page 29 of the report they give the % of people who got each question right.   In 2012 a full 75% of people got the question correct.  Thats a whole lot better than 50%.    Of course only 75% is not great cause that still means that 25% of people got it wrong. 

Now I notice that the article in The Economist says that only half of people "aged over 50"  got it right.   So maybe older people do poorer than the rest of the nation on that question?    Well if you flip back to page 28 on the report they break down how well people do on the test by age group.   They only have 3 age groups :  age 18-34, age 35-54 and 55 or over.    The groups got scores of 2.3, 2.9 and 3.3 respectively.   The 55 and older group did the best on the quiz.

I think The Economist was wrong in its report.    The actual FINRA survey report shows 75% of people got that question right.

I noticed that The Economist article actually said : "a survey found that only half of Americans aged over 50 gave the correct answers."     They used 'answers' plural.   Made me wonder if they were thinking of all 4 questions.   But people over 55 didn't get all 4 questions right.  

I  later checked out the comments in The Economist article and found someone already pointed out the error there.    They cited this different survey How Ordinary Consumers Make Complex Economic Decisions: Financial Literacy and Retirement Readiness  available at NBER which says in its summary : "only half of Americans age 50+ can correctly answer two simple questions about compound interest and inflation".   So in actuality its 50% of people who get TWO questions right.  Not just the interest rate question.    If you browse forward in that report down to Table 1 on page 26 they give results for every question.    The group age 50 and over got the 'numeracy' question right 92.9% of the time.   The under age 50 group got it right 91.3% of the time.    That same article points out that this set of financial literacy questions have become  standard questions used in multiple such surveys.

I'm puzzled why the FINRA survey shows only 75% o people got the question right while the other study at NBER showed 91+ getting it right.   Thats a pretty huge difference in results between two studies. 

In any case The Economist article misstated things and people aren't so shockingly bad at finance math after all.

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Do You Spend $33 a Year On Bread Twist Ties?

I saw an article yesterday from Planet Money titled $10 Billion Bread Battle: Twist-Tie Vs. Plastic Clip

[note: the original Planet Money article has since been corrected]

$10 billion?   Really?   That seemed odd.  Not sure how there would be a $10 billion market for items that probably cost less than 1¢ each.    Lets say every single person in America, roughly estimated at 300 million people, eats one loaf of bread every day of the year we'd get 300 million x 1 loaf x 1¢ x 365 or 300,000,000 x 1 x .01 x 365 = $1,095,000,000 or $1 billion.   Clearly thats a gross overestimate since we don't eat a loaf of bread per capita daily.  But my gross overestimate is already 1/10th the number that NPR cited.    Looking at it another way if they're right and the $10 billion dollar figure is correct then that equates to about $33 per year per person, hence my article title.

Where did NPR get this from?   They said it came from a Business week article titled Twist-Ties vs. Plastic Clips: A $10.6 Billion Battle of Tiny Titans


The article originally said :

U.S. unit sales for packages of bread, rolls, buns, English muffins, and bagels for a recent 52-week period totaled more than 7.2 billion (yes, we still eat a lot of carbs, Dr. Atkins notwithstanding). If we allocate half of those packages to clips, which sell for about $2.15 per thousand, and the other half to twist-ties, which cost about 80 cents per thousand, we’re talking about a $10.6 billion market,

(they've since modified it)

OK...

If you're quick you might already notice the problem there. 

7.2 billion units were sold.   7.2 billion is 7,200,000,000.   

The clips or ties cost at most $2.15 per  1000 units.   Therefore you can buy 1000 clips for $2.15.   We could also say they cost roughly 0.2¢ each.

You would need 1000 x 7,200,000 units  to cover the market.   You can buy that many clips for $2.15 x 7,200,000.  or $15,480,000.    Thats $15.5 million.    Worst case.

The market for clips or ties should be closer to $10-15 million.    They are off by a factor of 1000.

Remember I said the quick folks might have already spotted the problem?   Look at the bold/underline parts.   7.2 billion ... $2.15 per thousand ... $10.6 billion.
If you just look at the units there billion ... per thousand ... billion you can see their mistake.
They're basically taking billions / thousand and getting billions.   But the "per thousand" is a division operation and dividing billions / thousand gives us millions.

They instead approximated the price somewhere between the $2.15 amount for clips and 80¢ for twist ties so they're guessing average cost of $1.47.  

Lets look at it another way for a second quick common sense fact check.   The entire bakery industry has $30 billion in annual revenues.    I think its pretty clear that 1/3 of the bakery revenues don't go to pay for those little plastic clips, so clearly the $10 B figure is in the wrong ballpark.

I'm a little surprised that Businessweek would publish an article with a headline based on a math error.    I'm also surprised NPR would pick up the story without questioning it.   Does it not seem obvious that $10 billion is far too large of a number for something trivial like bread bag clips?   Maybe its not so obvious given how numbers like billion and trillion are thrown around daily yet are really hard to grasp the magnitude of them.

I'm sure most journalists can do math well enough and we all make occasional mistakes.   However it is alarming that a major publication like Businessweek would let a fairly big math error like this get through their editorial process and end up a article title.   Its also concerning that other journalists like those at NPR would perpetuate the error without catching it.

In the end this one was caught by commenters and fixed on the Businessweek article. 

Bottom Line:  We need to watch and question the numbers you see reported by the media.

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People Are Shockingly Bad at Simple Finance Math

The Economist has an article about financial education : Teacher, leave them kids alone

They start the article with this :

"HERE is a test. Suppose you had $100 in a savings account that paid an interest rate of 2% a year. If you leave the money in the account, how much would you have accumulated after five years: more than $102, exactly $102, or less than $102?
This test might seem a little simple for readers of The Economist. But a survey found that only half of Americans aged over 50 gave the correct answer. If so many people are mathematically challenged, it is hardly surprising that they struggle to deal with the small print of mortgage and insurance contracts."

Wow.  This is shocking to me. Can the results be accurate?    Are people really that bad at math or ignorant of basic finances?  


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How To FIgure How Much An Investment Grows Over TIme with Interest

On one of my older articles History of new car costs and average inflation a commenter said that $1500 would grow to over $3 million in 64 years with just 3% interest.   I'm not sure how they did the math or what mistake they made but with 3% interest you'd have $9946 after 64 years.  Nowhere near $3 million.

Here is the formula to see how much an investment will grow with a given interest return over multiple years :

Growth rate = ( 1 + [interest rate ] ) ^ # Years

The interest rate is expressed in decimal i.e. 3% interest is .03   So for example if you had 3% interest over 64 years that would make the growth rate :

= (1 + [interest rate ] ) ^ Years
= (1 + .03 ) ^ 64
= 1.03 ^ 64
= 6.631

Once you know the growth rate you can find the future value by multiplying your investment by the growth rate.  If you start with $1 then you'd end up with $6.63... $100 would give you $663, etc.

 Therefore if you start with $1500 and the growth rate is 6.631 then your investment after 64 years of 3% growth would be $1500 x 6.631 = $9946.50

In Windows operating system you can use the x^y key on the scientific layout of the calculator program.  The X^Y key is shown in yellow here :

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Low Cost of Living versus Higher Wages

One common idea in personal finance is that it is beneficial to live in an area that has a lower cost of living.   Keeping your expenses lower is a basic tenant of financial success.   Living in a lower cost area can have a huge impact on your finances.    The other side of this however is that wages are generally higher in the high cost areas and lower in the lower cost areas.    You could pit this as a choice between lower costs and higher income.   Whats better?   

Do you come out ahead living in a low cost city and earning lower wages or living in an expensive city with higher pay?

To examine this issue I decided to do a case study for one profession in a few cities.   I am arbitrarily picking both the profession and select cities to look at for my case study.

I'm going to look at one profession : Computer programmer.    I picked that because its close to my own career field and because I think its a relatively high wage job where pay rates also varies considerably from city to city.    If the wages for an occupation do not vary from city to city then its much more of a given that you'd do better in lower cost cities.   If your wages are relatively low then again it is much easier to come out ahead in a lower cost city.

I'm going to look at 4 cities that are in different cost categories :

Very expensive : San Francisco CA
Pretty expensive : Seattle, WA
Pretty cheap : Minneapolis, MN
Very cheap : Grand Rapids ,MI

Basically I chose these cities because San Francisco and Seattle are likely to have more programmers that get paid larger wage and then I chose Minneapolis and Grand Rapids as semi-random examples of lower cost cities to use as alternatives.    You might end up with entirely different results if you picked four different cities. 

Wage,  Housing and  Cost of Living

First lets look at how wages and cost of living compare for a computer programmer in the four cities.   Since housing is the largest expense, I'm going to pull that figure out as well.   I got average wage amounts for computer programmers for each city from the BLS Metro wage estimates for May 2010.  Median home prices are for Q3 of 2011 and I got them from the Realtor.org site from their metro median prices data.  (Direct file link).   Lastly I got the cost of living (COL) index figures from the Sperlings Best places cost of living site.

Here is the data :

	Wages	Median home	cost of living
San Francisco	$94,310	$491,000	185
Seattle	$92,840	$286,000	149
Minneapolis	$69,070	$160,000	108
Grand Rapids	$63,420	$111,000	84

Now if you simply look at pay rates proportional to home costs or cost of living index then everything falls in line.  Pay versus COL goes up with cheaper cities and the pay versus home cost increases as well.   we can express the ratios of Pay versus COL and pay versus housing as follows:

	pay/col	pay/home
San Francisco	$510	19%
Seattle	$623	32%
Minneapolis	$640	43%
Grand Rapids	$755	57%

If we simply stop there then it would be a given that Grand Rapids is the best city because your pay / cost ratios are the best there.   But real life is not so easy.    The ratio between pay and cost of living doesn't really mean all that much.   What really matters is the amount of money you have left over after your expenses.  

Lets look at an example of how that works : Consider two hypothetical cities A and B.   Lets say wages are $100k in A and only $50k in B.   Then lets estimate that the cost of living in A is 125%  more than city B so that the COL's are A = 225 and B = 100.  Wages / COL would be A = $100k/225 = 0.44 and B = 0.5   The wage / cost of living ratio is better in the cheaper and lower cost B city.   However what if your basic expenses are only $35,000 in city B and 125% more for $79k in city A.   At the end of the day when you take your wages minus total expenses you're left with only $15k in city B and $21k in city A.   You come out ahead in the more expensive city even though expenses are 125% more and wages are only 100% more.

With this thinking in mind its more important to look at how much money you're actually left with after accounting for wages minus expenses.

Disposable Income after taxes and housing


I'm going to figure an amount for the disposable income after figuring taxes and housing costs. This is an estimate of what a computer programmer would be left with in each city after paying taxes and a home mortgage.

I used MortgageCalculator.org to estimate the monthly payment for a $100,000 home at about $820 including principal, interest and property tax.   (note that property tax varies widely so this is a simplification on my part)   I then multiplied by 12 for a years worth of mortgage payments. This is the total housing cost in each city based on buying a median price home.   I am assuming 100% financing which isn't too realistic nowadays but it negates the issue of having to deal with varying size of down payments.

I used the tax calculator at Money Chimp to figure the federal income taxes assuming a married couple with 2 kids and only the one income.    I also added 9% of wages to the taxes to account for FICA and state taxes.   I know that 9% is not very accurate and state taxes probably amount to more on average, but I had to arbitrarily pick a figure so I just went with 9%.

	Wages	Tax	Home	Disposal
San Francisco	$94,310	$17,825	$48,314	$28,171
Seattle	$92,840	$17,472	$28,142	$47,226
Minneapolis	$69,070	$11,767	$15,744	$41,559
Grand Rapids	$63,420	$10,411	$10,922	$42,087

Now we start to see something interesting.    First lets throw out San Francisco since its obviously too expensive to come out ahead though the wages are highest there.    After you pay your taxes and mortgage the programmers living in Seattle are left with more money than those in Minneapolis and Grand Rapids.   Of course you still also have to spend money on various other things so that will likely eat up Seattles gains, right?   Lets take a look.  Here are the more detailed cost of living figures for Seattle, Minneapolis and Grand Rapids:

	Seattle	Minneapolis	Grand Rapid
Overall	149	108	84
Grocery	110	109	98
Health	116	102	95
Housing	243	106	55
Utilities	89	97	92
Transportation	114	110	96
Miscellaneous	122	114	93

If you look at the overall number or the housing umber that is where we see the largest variation.  Housing is almost 5 times as expensive in Seattle as it is in Grand Rapids.   But once you account for housing the other costs between cities only vary 10-20% more than not.   Housing cost alone inflates the overall COL considerably.   The cost of living differences with housing excluded are much less from city to city.

I'm going to use the Consumer Expenditure Survey to get national average estimates for how much households spend in the basic categories.   For example the CES says that the average spent on transportation is $7,677.    Using the national average as a baseline equal to 100 we can then calculate how much an average household is likely to spend on each category given the different cost of living index.   For example if the average for transportation is $7,677 nationally and people in Seattle spend 114 index on transportation then we can estimate that Seattle residents spend 114 / 100 * 7677 = $8,752 on transportation and likewise if the index for transportation is only 96 in Grand Rapids then we can estimate that people there spend 96/100 * 7677 = $7,370.    I use this logic to estimate the spending for various categories in each city and then sum up the totals. 

Here are the total average household spending estimates normalized to the cost of living index for each category for the cities :

	Seattle	Minneapolis	Grand Rapid	national
Grocery	$3,986	$3,950	$3,552	$3,624
Health	$3,662	$3,220	$2,999	$3,157
Utilities	$3,257	$3,550	$3,367	$3,660
Transportation	$8,752	$8,445	$7,370	$7,677
Miscellaneous	$8,932	$8,346	$6,809	$  7,321
SUM	$28,589	$27,511	$24,096	$25,439

As expected it does cost more to live in Seattle but not by a wide margin.   When you set housing aside the spending  in the other major categories does not vary as greatly.

Now lets put it all together and see how much you are left with after paying your taxes, paying a mortgage and then spending an average amount on other categories.   We can do that by taking the disposable income after taxes and mortgage figured above and then subtracting the sum of other spending in the last table.

	After tax & home	Other spend	Net Saved
Seattle	$47,226	$28,589	$18,637
Minneapolis	$41,559	$27,511	$14,048
Grand Rapids	$42,087	$24,096	$17,990

That 'net saved' amount is the bottom line you would be left after :

Wages - taxes - mortgage payment - sum of other spending = net saved

By this estimation you actually come out ahead in Seattle.    Surprised?

There are several things that should be noted and kept in mind.  

This won't happen for any occupation or any city.   As I said early on if your wages are much lower then you'll generally do better in the low cost city.  I'd much rather try to live on minimum wage in rural Michigan than in Seattle.    Where the jobs are matters too.   Just because housing is cheap in the Midwest doesn't mean you can find a job there in your field.  I'd rather be gainfully employed in high cost San Francisco than be unemployed in Michigan.    I used average wages, median home values and average spending for other categories, but individuals are not average.   Everyone's spending behavior is different and you should figure out how spending and costs would impact you rather than look at what the average American spends.

Remember how I picked a low amount for the FICA and state taxes?    You might now point out how that alone could throw everything off.   Being off 1-2% on the state tax rate would mean Seattle falls behind.  I would point out that Washington state is one of the few states with no state income tax.   So, figuring actual tax burden may put Seattle even further ahead.   It is more analysis than I care to do today and thats why I simplified it by picking an arbitrary number.    It is important to keep in mind that if you were to do a real comparison for yourself then you should really figure the actual tax burden for each city in question based on the state and local tax rates.

The points I'm trying to make are :
The answer isn't as simple as finding the lowest cost city or comparing the wage / cost of living ratios.   The more important factor is the amount of money left after expenses are taken out of wages.
You really have to scrutinize individual occupations in specific cities and there aren't any broad rules that tell us if you'll do better financially in a cheaper city or a higher cost area.
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Its OK to Round to the Dollar When Budgeting

Sometimes you'll see people talking about tracking your spending "to the penny" when discussing budgeting.   I don't know for sure if that is meant to be taken literally or not.   However I can confidently say that its not really necessary to track every cent of your spending.    It is OK to track your spending to the nearest dollar.   After you add it all up, rounding off the value of your purchases and expenses will be just about equivalent to tracking the exact numbers.

Lets look at an example of 10 figures.   Below are ten actual dollar value purchases from one of my credit card statements.  I compare the actual bill to the amounts rounded to the nearest dollar.

actual	rounded
$88.35	$88
$35.00	$35
$43.15	$43
$95.32	$95
$92.33	$92
$28.89	$29
$22.97	$23
$60.00	$60
$3.99	$4
$42.27	$42
sum	sum
$512.27	$511.00

As you can see after you add up the totals the difference is only $1.27 out of $512.27.

If you have 10 transactions then the most that those could be off by rounding to the nearest dollar is $5.

For example lets say you had 10 purchases all of $1.50   If you rounded those to the nearest dollar you'd round up to $2.   That would mean you add 50¢ for each transaction and you'd be off by $5 total compared to the actual purchases.    However the cents values of your purchases are almost always going to be randomly distributed more than not.   You won't have a ton of purchases with 50¢ in change.  You'll have several purchases of 90¢ or more and many of 10¢ or less worth of change.   They will tend to even out over a larger sample.

I looked at a set of almost 500 purchases in my credit card statements to date.   For various groups of numbers I compared rounding to actual figures.

Looking at groups of 30 purchases the most that the rounded figures were off versus the actual numbers in total was $2.54     For groups of 10 purchases the sum of the rounded values was at worst $1.78 less than the sum of the actual numbers.  With a larger group of 60 figures the impact of rounding versus actual was $3.52 in worst case.   

As a percentage basis the error induced by rounding was usually around 0.1% to 0.2%.    The worst case I found was off by 0.5%.

If you're doing a monthly budget then you may have 20 to 30 individual financial transactions to record.   If you round those figures then its likely the rounding will only change the totals by a couple dollars which will be less than 0.5% difference.  


Bottom Line : Rounding off your spending transactions to the dollar is not going to change your budget in a meaningful way.   Rounding can save you some time and make budgeting easier.

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The Great Pacific Garbage Patch : Is it really a Vast trash dump?

Note : Today's topic has nothing much to do with personal finances.   

Have you heard about the  so called Great Pacific Garbage Patch?   Theres a large amount of trash floating around out in the middle of the Pacific Ocean.   By some accounts there is a giant pile of trash the size of America floating in the middle of the Ocean.   If you picture this in your mind you get an image of a vast expanse of junk for as far as the eye can see.  

Sometimes when people talk about the Giant garbage patch you'll see close up images showing a bunch of garbage floating in water.   In fact you really only see close up images of floating trash or pictures of individual pieces of trash.   Worse yet if you do a Google search for images for "Great Pacific Garbage Patch" then you get a lot of pictures of piles of trash floating near beaches which certainly are NOT in the middle of the ocean.    If this garbage patch was so big and dense then wouldn't we be seeing real aerial photos of vast amounts of trash?   Why only close up or fake pictures?   The reason is that the amount of trash out there isn't all that much relative to the vast size of the ocean.    There aren't large clumps of junk nor vast areas covered in trash.  

How much trash is there really?    How dense is the trash really?   

From some accounts the garbage patch is supposed to be 2 times the size of Texas.   Or maybe not, it could be only twice the size of Hawaii.    Texas versus Hawaii is a pretty large margin of error in the estimates.  

How much garbage there is is another measure.   According to this report there is 5,114 g / km sq in the area.   I'm not sure how accurate that measurement is but its one of the only ones I could find.

Disclaimer:  I'm using rough math here.   I'm starting with estimates ranging from the size of Texas to the size of Hawaii so I think that rough figures are good enough.

For discussion sake lets assume that its twice as big as Texas and the 5,114 g/km sq figure is accurate.   Texas is 695,622 km sq. or twice that is 1,391,244 km sq total.  Then that would mean there is 7,114,821 kg or about 15.6 Million pounds of waste floating in the area.   From Wikipedia, : "Americans generate more waste than any other nation in the world with 4.5 pounds of municipal solid waste (MSW) per person per day" So per person we put out 4.5 pounds of trash a day. There are around 300 million people so thats 1.35 Billion pounds of trash a day.   The mass of the trash floating in the Great garbage patch is equal to roughly 1% of Americas daily trash output.   That could be a worst case scenario.    

Of course by comparing the amount of trash to American trash output I'm not meaning to imply that all the trash came from America either.   Many countries border the Pacific and contribute to the trash and much of the trash is from ships not owned by America.



Lets go back to that 5,114 g / km sq figure.   5,114 g in a Km squared is not a lot.    KM squared is a very large area.  Thats 1,000,000 square meters.  That means theres roughly 0.005 grams per squared meter.   A gram is actually a very small amount so 0.005 grams is extremely small.   A zip lock bag ways about 1-2 grams.  So we're talking about a piece of plastic which is about 1/200th to 1/400th the size of a 3" square zip lock bag.   That would amount to something about 30 sq milimeters.  Or a speck of plastic roughly 5x6 mm.

Lets see what a 5 mm x 6mm fleck of plastic looks like. 
Here the size of the average amount of trash per square meter compared to a penny: 

I put the speck of plastic in a field that is too scale proportional to 1 meter square and it looks like the picture below.  This gives you an idea of the density of trash in the Giant Garbage Patch. :

Well it kinda looks like that when I size the image so it can actually fit in this blog it makes the bit of plastic sooo tiny that you can't see it so I had to circle it in orange so something would actually show up.

One research expedition by the Algalita Marine Research Foundation traveled 2,000 nautical miles across the Atlantic and reported  "During the expedition, 100 pieces of floating marine debris were sighted."  On average thats 1 item spotted per 20 miles traveled.   Keep in mind this is a research foundation which is trying to bring attention to the problem so they aren't likely to under report the amount of trash.  Hardly a vast see of junk.    But again it should be stressed that much of the trash in the ocean is small bits and a lot of it is below the surface.  

There isn't a vast giant pile of trash floating in the middle of the Pacific Ocean.    There is however tons and tons of plastic bits that are floating out in the ocean.   The ocean his so vast that those little plastic bits are more often tiny bits of plastic or maybe a single discarded mylar balloon every few miles.

Please don't misunderstand me.... any amount of plastic floating around in the ocean is not a good thing.   The more plastic out there the more harm it does to fish and wildlife and contaminates the environment.

Lottery Odds and an Odds Calculator

Do you know the chances of  winning the multi million jackpot prize in the lottery?     The obvious answer is 'very small'.    However I'm talking about the actual mathematical probability. 

I would assume that most if not all state lotteries publish the odds of winning their lottery games on their website.   If you want to know the odds of your state lottery then I'd check out their website.    It should probably be posted there somewhere.   You could also do a google search for keywords including "odds winning" and your state lottery.   e.g. for the Wisconsin state lottery search for "Wisconsin lottery odds winning".

The odds for the multi-state Powerball lottery are published on their site.  The odds of winning the Powerball jackpot are 1 in 195,249,054.   They have smaller prizes with crappy odds too.   For example the odds of winning $4 is 1 in 123.   Clearly the Powerball is a poor gamble if you look at the odds.

If you want to know the odds of any lottery style game then you can figure them yourself using the lottery odds calculator.  

You can verify the odds of the Powerball jackpot yourself by using the calculator.   The Powerball is a 'multi-pool' lottery game since the bonus powerball is from a separate group or 'pool' of balls.   There are 59 balls in the main number pool and you need 5 of 5 to win and then there are 39 balls in the secondary pool and you need 1 to win. Here's what it looks like using the calculator:

Of course I don't think its really necessary to verify the odds that the lottery program quotes.  Its hardly something they'd lie about since its easily verified and such blatant fraud would serve nobody.  

Why do lottery odds matter?   Well for one you should realize how very high the odds against winning really are.   Hopefully we've all heard by now that winning the lottery is very very very rare occurrence and you're more likely to be hit by lightning.    Another reason to know the odds is so that you can pick the lottery games with the better chances.   If you're going to play the lottery (for fun only) then you should at least pick the one that has better odds. 

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Why a $1,000,000 Prize Is Often Only Worth $725,000

McDonalds is starting up their Monopoly game soon.  Doughroller let us know  McDonald’s Monopoly Game is Back!    while Jim at Bargaineering also told us  How To Win McDonald’s Monopoly Game
The grand prize for the Monopoly game is $1,000,000.     But there is an ( * ) asterisk by that $1,000,000 prize.   You don't get a lump sum of 1 million dollars.  The prize is actually paid out in $50,000 yearly for 20 years.   This is not uncommon for major prizes.  Most lotteries pay out prizes like this.  

Getting paid $50,000 a year for 20 years is not the same as having $1,000,000 today.   First of all its common sense, everyone can see more value in having $1M today than $50k a year.   (Some people may prefer to get the money spread out so they don't blow it all at once, but thats a different matter.)    Inflation and the effects of interest are the main reason that money in hand is worth more than money spread out over years.   Lets look at the $50,000 paid out on year 20.   Thats not worth $50,000 today.  Clearly $1 in 2031 will not buy as much as it does today due to inflation.   If you assume 3% annual inflation then $50,000 in 2031 will be equivalent to about $27,683 in todays dollars.   Nearly half as much.


One simple way to figure out how much equal payments over time equates to in todays dollars is to find out how much an annuity would cost.    You can buy an annuity that pays you $50,000 a year for 20 years.   This kind of annuity can be bought with guarantee that each year will be paid regardless of how long you live so its not like other immediate annuities that depend on your lifespan.   The cost of that kind of 20 year fixed annuity is a good approximation for the value of that kind of payout.

You can get quotes on annuities at immediateannuity.com

From there we can see that a Guaranteed Income for a 20-Year Period Certain Only ("20PC")
paying $50k a year (4167/mo) would cost  = $724,696.


The $1,000,000 prize from McDonalds Monopoly game is equivalent to a 20 year period certain annuity paying $50,000 a year which would cost $724,696.   Therefore the McDonalds Monopoly grand prize of $1,000,000 really has a cash equivalent value of $724,696.

But its still a fun game.

How Much Does Watering My Lawn Cost?

One of our recent purchases was a sprinkler system as part of our landscaping project. I've never watered my lawn all that much, but now with the nice new sod and landscaping I'd like to keep the plants from all dying and having it look bad and wasting that investment. Anyway, we'll want to water our lawn and plants with the automatic sprinklers. I figured I should find out how much it will cost.

Our water bill covers 2 months and we just got the last bill. So I won't be able to see the cost of watering the lawn for a full 2 months. I wanted to estimate the cost before hand so that we don't get surprised by a very large bill.

What water costs us:

My city charges $2.5 about / ccf for water and sewer charges (1 ccf =748 gallons). Our water costs around 0.33 cents per gallon. If we use significantly more water then we could hit the next tier of rate and it would get up to about $3 / ccf or 0.4 cents/gallon.

Estimate #1: 30 minutes a day x guesstimate on gpm
First estimate is based on simply running the sprinklers 30 minutes a day and guesstimating the amount of gallons per minute the system would put out. I don't know exactly what kind of hardware they used or what they are rated at but you can find sprinkler heads on the net. This Rainbird sprinkler head says it uses 2.5 to 4.3 gallons per minute (gpm). This Rainbird model does 2.1 to 3.2 gpm. These Hunter sprinkler heads put out anything from 0.3 to 14 gpm. So the range of GPM per head is pretty wide. I believe we've got the smaller type heads that are probably more like 2-4 gpm. There are 5 heads in each zone in our lawn. So I guess we'd be using 10-20 gpm. If the lawn is set for 30 minutes of watering total then that would be 300-600 gallons of water per water. That is 2100 to 4200 gallons of water a week. At a rate of .33 to .4 cents per gallon that would come to about $6.93 to $16.8 per week or $27.72 to $67.20 a month.

Estimate #2: 30 minutes x typical gpm
This page says that the suggested GPM for a lawn sprinkler is 8 gpm. With 30 minutes of use a day that would be 240 gallons a day. Thats $23.76 to $28.80 a month.

Estimate #3: 1" per week method
I probably shouldn't just water the lawn a full 30 minutes a day. AllAboutLawns recommends watering your lawn about 1" per week. For 1000 sq. ft. of lawn that would be about 83 cubic feet of water. A cubic foot of water is 7.48 gallons so watering a 1000 sq ft lawn 1" would take about 623 gallons of water or 2,492 gallons a month. So we'd be spending around $8.22 to $9.97 a month to water our lawn at the rate of 1" a week.

Given the 3 different estimates I come out with estimated costs ranging from $8.22 to $67.20 a month. I think its a pretty good bet that the actual cost will probably end up somewhere in the middle in the $10-$30 range.

Of course the exact amount we spend will depend on how much we decide to water the lawn. If we have it run 2 times a day every day then that will cost more than if we run it once a day every other day.


What do others pay?

This discussion on Gardenweb.com has some people citing their lawn watering costs.
There is one person paying $150 a month for 7000 sq ft of lawn. Another person spends $100 to $250 a month for 1/3 of an acre.

This article on Slate estimates that average American lawn uses 21,600 gallons a year. AT my 0.33 to 0.4 cent rate per gallon that would be about $71.28 to $86.4 per year.


Photo by °Florian

Comparing Two Investments

Lets say you were offered two investment choices either A or B as follows:

Option A

You get 5% fixed interest on your investment for a 10 year period. You might get this kind of investment with a CD or a bond.

Option B

You get 10% interest 9 out of 10 years but one year you see a 40% drop in your investment. The average annual rate is 5%. The average of +10%, +10%, +10%, +10%, +10%, +10%, +10%, +10%, +10% and -40% is +5%. I don't think anyone out there sells investments like this. But its theoretically possible that you could see this kind of return trend in a stock market investment.

If you put $1000 into each of these options which do you think would give you more money in the end?

Surely the annual average rate of 5% is going to give you the same amount in the end compared to the fixed 5%, right? No, you might have guessed that this is a trick question. In fact that 40% drop really undercuts all your growth. While the annual returns might average to 5% you're losing much of your compound growth and its harder to dig out of a hole.

With option A you would have $1,629 after 10 years. Option B would leave you with only $1,415.

The compound annual growth rates are option A : 5.0% and option B : 3.5%.

Whats cheaper a shower or a bath?

I always take showers and for whatever reason I had assumed that a shower wasted more water than a bath. But then I came across a page on the web that claimed otherwise. So I decided to run the math for myself and figure it out.

Shower:
A typical shower would run about 10 minutes. With a shower head that flows at 2.5 gallons per minute that means you'd use 25 gallons of hot water for the shower. Water costs 1-2¢ to heat. Therefore a 10 minute shower would cost you 25-50¢.

Bath:
A typical bathtub has about a 60 gallon capacity. However some of that area will be displaced by the person in the tub. Exactly how much area your body will displace will depend on how big of a person you are. However we can at least look at the average. The average American is about 75kg so they would displace roughly 75 liters or about 20 gallons. So you'd have to put about 40 gallons of water in a tub to fill it with a person. To heat 40 gallons of bath water would cost 40-80¢.

A typical shower is cheaper than a typical bath.

It will vary of course depending on exactly how long your showers are, how much water you use in a bath, how big your body is, etc. But on average it appears that showers are more frugal for average adults.

How much exactly would an Autocirc1 save in energy costs?

Previously I discussed a hot water recirculator pump called the Autocirc1 in the article Autocirc pump to save water, money and get hot water faster.

The Autocirc1 is made by Laing. The Autocirc1 pump is designed to keep hot water in your pipes at all time. The pump saves money by not wasting hot water so the manufacturer claims that it will save you on your energy costs. However the pump keeps the water in your pipes relatively hot most of the time and this will cost you money.

A commenter Tony said:

"I am not convinced that this device will really save money for many people. By keeping hot water in the pipes, constantly drawing it from the tank when the pipes get cool, you're forcing the heater to heat more water than it would otherwise do. That will reduce or even outweigh the savings from the water consumption."

Thats a good point and I wanted to get a better idea for myself about how the Autocirc1 would or wouldn't save money.

So the question today is: How much money will an Autocirc1 actually save and how do you figure the savings?

Before I begin, let me state specifically that these are very rough numbers and I'm making estimations here. There are some variables I'm ignoring on purpose to simplify things. I'm doing a fairly crude estimate on purpose here because I can't realistically do a perfect model or it gets way too complex.

This pump keeps hot water in your pipes all of the time. This means you get hot water at your faucets instantly and you don't have to run the water for a minute or so to get hot water. The maker of the Autocirc1 claims it saves homes $100 to $300 annually. But unfortunately they do not go into specifics on their website about HOW you save energy.

First of all you have to look at how it saves money. The key concept is that it takes more energy to heat water up to the 125F that your hot water heater keeps it at than it takes to keep water at a 85-95F level.

Normally water comes into your home at 40F and then your hot water heater heats it up to 125F. When you use some hot water in your home and then turn off the faucet all the water in your pipes is still hot and just sits there. That water cools of pretty quickly and is effectively wasted. The longer your pipes are the more water will be wasted. In addition to not having to heat the water you also don't have to pay the water utility for the water itself.

On the other hand, with the Autocirc1 it works to keep the water in your pipes at 85-95F all of the time. That means it only has to heat up the same amount of water by 10F degrees periodically when it cools down. Its a limited amount of water that it is heating as well.

Lets look at a couple families with different homes and different situations. These two examples are meant to represent two extremes and I think most homes will fall somewhere in between.

I start with some assumptions. First of all I assume that it costs 2¢ to heat a gallon of water by 80F (as discussed previously). I also then assume that it costs about 1/4¢ to heat a gallon of water by 10F. I assume that municipal water bills cost 0.2¢ per gallon of water on average. I assume that the pump recirculates the water 3 times an hour average.

The Smith House: Their hot water pipe is 3/4" and their hot water heater is about 90' from the bathrooms on the other end of the home. They have an electric hot water heater and pay 11¢ a kWh. Their hot water pipes hold about 2 gallons of water and it costs them 2¢ to heat a gallon of water 80F.

With normal pipes:
Normally you run water 20 times a day spread out about evenly through the day. That means that any time you use hot water you will pull 2 gallons of hot water out of the tank which then fill the pipes. You then use up some water and leave those 2 gallons of hot water sitting in your pipes. That hot water then cools down over time. This is effectively 2 gallons of hot water you're wasting every time you use hot water. A gallon of hot water takes the Smiths about 2 cents to heat from 40F to 125F using their electric water heater. So you're wasting around 80 cents a day. Thats $292 a year. You're also wasting 40 gallons of cold water that you run down the drain waiting to get hot water at the tap. You have to pay your water bill and that water costs money. At 0.2 cents per gallon that amount of water would run you about $29.20 a year in extra water bills. So total cost is $321.20

With the Autocirc1:
Now lets say you have the circulator setup. It keeps the water in your pipes constantly at 85-95F. The circulator pump has to kick on every 20 minutes to circulate that water. So in effect you're heating up 2 gallons of water 10F degrees every 20 minutes all day. You have the timer setup so it runs 16 hours a day and shuts off when you're asleep. That means you're heating it about 48 times a day. That would cost about 24 cents a day or about $87.60 to heat the water.

The Autocirc1 would save the Smiths $233.60 per year.

The Jones House: This house is the same design as the Smith home. But the Jones family is a couple with no kids who uses their hot water faucets just 6 times daily.

With normal pipes: Normally they run the water 6 times a day at 2 gallons each. It costs them 2¢ to heat the water and 0.2¢ per gallon to buy it from the water utility. They waste 12 gallons of hot water a day or about 4,380 gallons a year. This costs them a total of $96.36 a year.

With the Autocirc1:
Their costs with the Autocirc1 would be the same as the Smith family which were $87.60 a year.

Total difference for Jones family would be $8.76 savings per year with the Autocirc1.

Keep in mind that these are very rough calculations and the figures will vary a lot based on the exact variables. If you vary the size of the pipe, water costs, electricity or gas costs, and average ground temperature of the water than that will impact the figures.

How did Laing get their numbers?

On their website Laing says that the Autocirc1 will save people energy costs in the $100-$300 range per year. They have a study they did to come up with these numbers. Their website however doesn't give the specifics on how they figured it. About their study they say: "Above summary based on study and analysis prepared by Edward Saltzberg and Associates, consulting mechanical engineers. Copies of this detailed analysis are available on request from Laing Thermotech, Inc." So I went ahead and sent them an email to ask them for a copy of that study and they quickly sent me it. I looked through their study to see how they figured the savings. They used the same basic ideas that I did. The Autocirc1 would save you money by not having to heat the water and based on water bills but it would cost you money based on keeping the water in the pipes relatively hot.

I'm not going to go through their entire study line by line or examine everything they did. If you want to look at their study then I'd recommend you just email them and ask for a copy. I will say though that it seems their conclusions are fairly realistic and I don't see any major faults in it, but it is based on certain set of assumptions.

They figured that a family would waste about 34 gallons of hot water daily. They are looking at a family of four and assuming they'd use the shower 4 times daily and sink uses of about 11 times a day. Thats a fairly heavy water use so if you have a small family and/or use water infrequently then your experience will differ.

They assume a water cost of $2.02 / 100 cu ft and $1.35 / 100 cu ft. Theres 748 gallons in 100 cu ft so this equates to about 0.2¢ for water and 0.1¢ for sewer. Those assumptions are in line with average water costs, however water utility cost varies a lot from city to city so again your circumstances may differ.

They state that heat loss from a 3/4" copper water pipe is 25 BTU per hour per linear foot for uninsulated pipe and 10 BTU /hr/ft for insulated pipe. This is a key piece of information for the calculations. With this number you can easily figure the cost of keeping the hot water warm in the pipes. With this you can figure the costs pretty easy to operate the Autocirc1.

Lets say your water pipes are uninsulated and 60' long and you keep the Autocirc1 on 16 hours a day.

= 60 ft x 25 BTU /hr /ft x 16 hr/day x 365 day/yr = 8,760,000 BTU /yr

There are 3413 BTU per kWH. So that means you'd be using 2566 kwH a year or about $256 a year with electricity of at 10¢ /kwh. There are 100,000 BTU in a therm so it would take 87.6 therms and if therms are $1 each then this would cost about $87.

For insulated pipes the costs would be 40%. So that would be $102 for electric and $34 for gas.

From Laing's study the cost of keeping the water in the pipes hot would be $34 to $256 for 60' of pipe.

On the other hand they are figuring that your water savings are about 12,000 of hot water per year. With hot water costing 2¢ to heat and 0.3¢ for utility costs thats about a $276 cost for the wasted water.

My methodology and that used in the Laing study differ a bit. But it is clear that the savings from an Autocirc1 will vary a lot depending on the usage level of home. The more water you use and more often you use your plumbing then the more the Autocirc1 would save. However if you do not use your plumbing very frequently then the Autocirc1 may not really save you much if anything. And any application of an Autocirc1 is assuming that the home has fairly long pipes running between the hot water heater and the sinks.



Some references:
Online discussion on Autocirc savings
BTU conversion figures

What does it cost to heat a gallon of water?

I found this site Ask Mr. Electricity that has a calculation of how much it costs to heat water with a hot water heater.

Bottom line is that given their calculations, it costs about 1¢ to 2¢ to heat a gallon of water.

The exact amount will depend on the efficiency of your hot water heater, whether you use gas or electric and exactly what your electric or gas costs are.


From the Ask Mr. Electricity site:

"Energy required to heat a tank of water

• A Btu, or British thermal unit, is the amount of energy needed to raise one pound of water from 60°F to 61°F at sea level. (Wikipedia)
• A gallon of water weights 8.33 lbs.
• If the incoming water is 60°F and we want to raise it to 123°F, that's a 63°F rise.
• Heating a gallon of water thus requires 8.33 x 63 = 525 Btu's, at 100% efficiency.

Cost to heat water in a gas tank

• A typical gas tank water heater is only 59% efficient. So it takes 525 ÷ 59% = 890 Btu's to heat a gallon of water in a gas tank.
• One therm is 100,000 btu's. So one Btu is 0.00001 therms. (Pacific NW Natl. Lab.)
• 890 Btu's is 0.0089 therms.
• So we've got 0.0089 therms to heat a gallon of water, or 0.0089 x 40 = 0.356 therms to heat a 40-gallon tank.
• At $1.42/therm, it costs 0.356 x $1.42 = $0.51 to heat a 40-gallon tank.
• Another source comes up with a similar figure: 0.40 therms for the tank (based on 0.11 therms to heat 11 gallons of water. (Multi-housing Laundry Association)
• MHLA also says it takes 3.3 therms to keep 11 gallons hot for one month.

Cost to heat water in an electric tank

• A typical electric water heater is 90.4 to 95% efficient. Let's call that 92.7% on average.
• So it takes 525 ÷ 92.7% = 566 Btu's to heat a gallon of water in an electric tank.
• One kWh is 3413 Btu's, so one Btu is 0.000293 kWh.
• 566 Btu's x 0.000293 kWh/Btu = 0.166 kWh.
• So we've got 0.166 kWh to heat a gallon of water, or 0.166 x 40 = 6.63 kWh to heat a 40-gallon tank.
• At $0.11/kWh, it costs 6.63 x $0.11 = $0.73 to heat a 40-gallon tank."

The two keys they had were that it cost $0.51 to heat 40 gallons using gas or $0.73 using electric. Thats $0.01275 per gallon for gas and $0.01825 per gallon with electric.

Calculating rate of return on rental property investments.

The three elements of a rental property return are: the cash flows from rents, the appreciation of the property and the decrease in principal due to principal payments. If you add these three elements together you get your returns. To figure the value of an investment you need to look at the value of the returns versus the value of money you put into the investment. So the return on investment (ROI) from the investment is returns / equity.

I'm going to present a simple way of figuring your return rate on a property. I'm not considering tax implications just to keep it a bit more straight forward. The example property I'm using is not a realistic property for most markets and I only use it for example purposes to show how the math works.

Lets look at the 3 separate return elements:

Cash flows are real receipts of cash from rents minus your expenses. You would figure your cash flow by subtracting all your annual expenses from your annual rents.

Cash flow = rents - expenses

For example, lets say you bought a duplex for $100,000 with a 6% fixed 30 year loan $20,000 down. Your monthly mortgage payment is $480 for an annual total of $5,760. Your property tax might be $1,050 and insurance of $400. Since you have a single meter pay the water bill which runs $80 every month or $960 a year. You had one vacancy and you paid $50 to advertise the property. Your total expenses for the year are $7,260. Your rents are $400 per unit and you had 1 month vacancy. So you collected a total of $9,200 rent for the year. Your cash flow for the year would be : rents - expenses = 9200 - 7260 = $1,940

Appreciation in the property is generally going to be an estimate of unrealized gains. Because of the cost you don't want to get professional property appraisals every year but you can use basic gauges of value to estimate the value. You could use a website like Zillow.com or skim the prices of properties currently selling at Realtor.com Realtor.com also tracks median home values for large markets and you could use those general numbers as a estimate of what your property may have increased (or decreased).

For example lets again look at the duplex you bought for $100k. If you look on Zillow and they say it is now valued at $105k and Realtor.com shows median prices in your area increased 5.2% then you can estimate that the property appreciated about $5000 for the year. But again this is just an estimate. If you go and try to sell the house you may or may not be able to get that price.

Reduction in principal is through the principal payments of the mortgage. Part of your mortgage payment will go towards principal (lets ignore interest only loans). SO at the end of the year you'll have a lower principal balance then at the start. At the start of your mortgage term the amount of the mortgage payment going to principal will be fairly small compared to the payment amount. But towards the end of your loan, your payments will be mostly principal and this amount can matter a lot. To figure your equity increase you need to look at your mortgage statements. Normally your statement will tell you the outstanding principal. Or you can also look at the original loan paperwork which ought to include a table of amortization showing the amount of principal paid on each month.

For the example duplex with a $100k loan you had $20k down so you start with $80k principal. After one year your mortgage payments would have put $982 towards principal. So your increase in equity is $982.

If you combine the cash flow, the appreciation and the reduction in principal then you have your total return for the year. To figure your return on investment you divide your investment by the return.

Return on Investment = (Cash flow + Appreciation + equity increase) / Equity

For our example duplex your cash flow was $1,940, the appreciation was $5,000 and the equity increase was $982. You put $20,000 so that is your equity. So that gives us:
= (cash flow + appreciation + equity increase ) / equity
= (1940 + 5000 + 982) / 20000 = 6176 / 20000 = .30 = 30%

That 30% return sounds great. However realize that this is not realized gain and doesn't represent cash in your pocket. The $1,940 in cash flow from rents is real cash in hand. However the appreciation and increase in equity is stuck in the value of the property and isn't realized. To obtain those gains you would have to sell the property. When you sell the property you'll probably have to pay realtor commission to sell it and you may also have to pay capital gains taxes. Another reason you're showing 30% return with this example is that the property is highly leveraged so you're taking risks. If you were unable to rent the property for a few months then that would eat all your cash flow, or if the property depreciated a small % then your return could easily be negative.

To get a view of the realized gains you could look at just the cash flows. If you just look at the real cash gains then your ROI would just be = cash flow / equity
In this case thats $1,940 / $20,000 = 0.097 = 9.7%.

To determine the real return you would have to include the cost of selling the property.

Lets look at another example where the returns aren't good. Lets consider the same property bought for $100,000 with 20% down. Lets say you had the same basic expenses but you had to replace a failed water heater for $550 and when the one unit was vacant the renter didn't pay 1 month rent and it took 2 months to rent it so you lost 3 months rent. That makes your expenses $550 more and your rents $800 less. So while before you had rent of $9200 and expenses of $7260 now you have rent of $8400 and expenses of $7810. So your cash flow = rent - expenses = 8400 - 7810 = $590 Lets say the property was in Little Rock Arkansas which has seen about 0.8% appreciation in the past 12 months. SO if the property started at $100k and increased .8% then it would have appreciated $800. Your principal reduction would be the same at $982.
So for this example you'd have:
= (cash flow + appreciation + equity increase ) / equity
= (590 + 800 + 982) / 20000 = 2372 / 20000 = .11 = 11%

Thats still not a bad return by any means. But what if the expenses ran over another $1000 or if the property didn't appreciate or depreciated as many markets are doing right now. With a little bad luck or a bad market you could actually see a negative return.

Generally you'll have positive returns from rentals in the long run. But you should measure and watch your return rates to make sure your property is giving a good return on your investment dollars.

How to evaluate the return of energy saving home improvements.

Lately I've talked about some home improvements that can help save energy costs. I installed compact fluorescent lights, I bought a programmable thermostat, I installed a water saving device on my shower, I use an electric mower and I've bought a smart power strip. Each of these purchases help save energy costs and give me an ongoing return through lower electricity bills. But they also cost money to buy in the first place. So how exactly do I tell if the energy savings of an item is worth the cost of purchasing it?


I would evaluate energy saving purchases in two ways. First you can look at the annual return rate and payback period. Second you can calculate an estimated rate of return on the investment.

Figuring a Payback Period

This is the simpler method. Basically all you do is figure out how many years it will take to recoup your initial investment. To do this you divide the initial cost by the annual savings. For example if you could spend $150 today to save $50 a year then you can divide the cost by the annual savings or 150 / 50 = 3 years.

Payback period = initial costs / annual savings.

If your payback period is 1-3 years then thats probably a good buy. Payback period can be pretty useful if you're comparing the purchase of multiple alternatives.

Lets look at some examples:
I discussed previously that buying compact fluorescent lamps for my home is saving me about $61 a year. I paid $50-100 for those initially. If we assume the higher cost of $100 then the payback period is: initial cost / savings = 100 / 61 = 1.6 years payback period.

I also bought a shower attachment for $30 that I figure is saving me $20 a year. For that purchase the payback period is = initial cost / savings = $30 / $20 = 1.5 years payback period.

If I compare these two purchases the shower attachment is marginally better with a payback period of 1.5 versus 1.6 for the CFLs. So if I had just $30 to spend then I'd be a little better off putting it into the shower attachment.


Estimating the Annual Rate of Return

For larger purchases that have a longer payback period it might make more sense to look at the annual return rate over the life of the purchase. Buying a large improvement such as a new efficient furnace or a solar array is essentially an investment so you should figure the rate of return on that investment and compare it to other investments.

TO figure what an improvement returns as an investment you have to look at what it will net you financially. Basically with an energy saving improvement you have an item you're buying for a certain amount today which will then give a fixed annual return for a number of years. For example I might pay $150 for an improvement which then saves me $50 a year in electricity and lasts 5 years. If I just took that $50 each year and sat on it at 0% interest then I'd accumulate $250 in a 5 year period. So my $150 investment turned into $250 over 5 years. We can use the formula for compound annual growth rate (CAGR) to figure the rate of return. The formula for CAGR is:

% return = ( (FV / PV ) ^ (1 / # years ) ) -1

For the example that works out to ( ( 250/150 ) ^ (1/5) ) -1 = (1.66)^.2 -1 = 1.107 - 1 = 10.7%

You then have to compare that to what else you could have done with the money. If I had $150 in the bank right now I could easily throw it into my high yield savings account and make 3.5% interest.

For this example paying that $150 will end up netting me a 10% return over 5 years. Thats a good return rate compared to 3.5%.

As a general process for figuring the rate of return on an energy saving investment:

First of all I determine the annual energy savings of the item. This depends on the item you are buying. Hopefully there is enough information on the type of improvement that you can figure the savings. If you are buying an appliance you can compare the energy guide documentation which will tell you the annual energy usage of the item.

Second I determine a lifetime for the item. The lifetime of the item will depend on the nature of the item. I basically take an educated guess to estimate the lifetime roughly based on how long I would expect the item to last. A small item I might figure a life of 5 years. For a large appliance I'd pick a 10 year lifetime. If the item is a major improvement such as a new furnace or something like a solar panel then I might go with 20 years.

Then you simply run the CAGR calculation using a future value of the annual savings * lifetime of the item.

That gives us an equation of:

expected % return = (( annual savings * lifetime in years / cost ) ^ ( 1/lifetime in years) ) -1

If you are not certain on the values then you should run the equations for the minimum and maximum estimates so that you can get a range. For example if you think the item might last 10-20 years then run the equation for 10 years and again for 20 years.

Note that I'm making a couple assumptions in order to simplify the calculation. I'm assuming that the item I buy is not going to retain any costs. In other words I assume it depreciates completely. Basically I figure if I buy a new fridge then over a number of years that fridge will wear out and basically be worthless at the end of its life. The other assumption I'm making is that there is no difference in tax impact from the item. This isn't true exactly but it makes the calculation and comparison simpler.

Lets look at a couple examples:

Example #1 buying a heat pump:

I'm considering buying a new heat pump furnace. For example purposes let say the heat pump costs $5000 to buy and have installed and that I will save around $300 to $500 a year in energy costs. I also figure the heat pump should last me about 10 years minimum.

Given the formula:
expected % return = (( annual savings * lifetime in years / cost ) ^ ( 1/lifetime in years) ) -1
We plug in the numbers for the minimum case to get:
return = (( $300 * 10 / $5000) ^ ( 1/10) ) -1
= .6 ^ .1 -1 = .95 - 1 = - 5%
And the maximum case is :
return = (( $500 * 10 / $5000) ^ ( 1/10 ) ) -1
= 1 ^ .1 - 1 = 0%

So for this example I'd be facing a -5% to 0% return on my money.

The choice of a 10 year lifetime was pretty conservative and its possible the heat pump might last 20 years.

If I figured a $300 annual savings for 20 years then it would be :
(( $300 * 20 / $5000) ^ ( 1/20) -1 = 1.2 ^ .05 - 1 = 0.91%
or at the $500 annual savings over 20 years is :
(( $500 * 20 / $5000) ^ ( 1/20 ) -1 = 2^.05 -1 = 3.5%

Therefore overall if we buy a furnace for $5000 and expect it to give an annual energy savings of $300 to $500 and the furnace will last 10 to 20 years then our expected rate of return on the investment is -5% to 3.5%. I can get 3.75% right now in a CD so this isn't a good investment.