Announcing The Value of Simple

September 28th, 2014 by Potato

By now you all know that I’ve been working on an investing book. I’m pleased to announce that the title is The Value of Simple: A Practical Guide to Taking the Complexity Out of Investing.

I’m aiming for a December 1 release and I’m really excited about it. I’ve put a lot of work into refining the book and testing it out with readers (novices and experts) to make sure it works. I even like love the title.

Briefly, The Value of Simple: A Practical Guide to Taking the Complexity Out of Investing is a plain-language guide to implementing an index investing strategy for Canadians. With a focus on developing good processes to minimize the room for human error and step-by-step instructions, the book walks investors through the elements of managing their finances for the long term: how they can determine an appropriate asset allocation, devise a savings plan, stick to it through automation, track their investments, and deal with the inevitable issue of taxation. It provides tools and templates, along with default suggestions and rules-of-thumb to help prevent analysis paralysis and get investors started as soon as possible. Moreover, it directs the reader to focus on what can be controlled, to minimize effort and complexity.

For the average investor, a low-cost index investing approach is the easiest and simplest method available, and also provides the highest chances of long-term success. While there is a lot of material available on why investors should choose passive approaches over high-fee active mutual funds and what passive investing products exist, the average investor is at a loss on how to implement a passive index investing plan.

Investing doesn’t have to be complex to be successful. Indeed, simple solutions are valuable and are more likely to succeed in the long term. This book will guide you through implementing those simple solutions.

There is a separate webpage for the book (click here!) where you can find more details and pre-order it (and soon, purchase it). You can also sign up for email updates below (and I promise to only send a few):



I Am Not Good At Marketing

September 26th, 2014 by Potato

The book is very nearly done. The text is all in there and has had multiple runs of editing. Now it’s down to formatting all the little things, remastering a few images for print, getting the cataloging-in-publication data, the cover art, etc.

I’m proud of it — I think it will truly help people get started at investing, and covers a lot of important elements that are not covered by the books that are currently out there. While I usually have a lot of problems with self-promotion, I can think of the book as being separate from me, as a thing I can promote and herald without it being self-promotion in my damaged mind. But I’m still not particularly talented at it.

I can do the Fermi estimation and figure that there are millions of Canadians out there between 24 and 60 who could really benefit from this book. Yes, many won’t need it; others won’t invest on their own no matter how helpful the book; some are in debt and in no position to use it. Even if just 5-10% of them need it and would use it though, that’s a big market.

And I have no idea how to reach it. The simple fact is that I am not good at marketing. I can maybe write decent copy if I focus on not letting the loquacity run away from me and give it a few revisions. But that depends on having people actually there reading something, and I don’t know how to get to those people in the first place.

My big hope is that everyone who reads it will love it as much as my beta readers did. That they will recommend it to their friends, family, and frenemies. Sadly, people don’t talk about personal finance and investing. Even if I put a copy into someone’s hands and they adored it, to the extent of writing me a little email about how it totally opened their eyes to investing fees and changed their life, the odds are that they will not tell anyone else about it*. For whatever reason, vampire bondage erotica is a more acceptable dinner table, coffee with friends, or book club topic than personal finance. So I can’t rely on word-of-mouth to spread the news of how awesome and helpful the book is.

But beyond word-of-mouth, what have I got? I tried contacting some people in the media. I’ve had online interactions with Rob Carrick, Ellen Roseman, and Melissa Leong in the past when I wasn’t trying to sell them anything (not necessarily deep ones — moreso with Ellen and Rob than Melissa), so I started by contacting them. They were polite, but it wasn’t very promising. There are other people I can try to contact, but those would be completely cold calls. Somewhere I saw a suggestion to get some freelance articles in the paper or a magazine to build name recognition before a book release, which sounds like suggesting that to successfully sell your book, you start with having a past bestseller first — the book started because Adam Mayers didn’t want my how-to articles for the Star! So the media’s a bust.

Advertising? I got a free credit for Google AdWords a few years ago and I tried advertising for the predecessor book. The ads were a complete waste. Maybe subway posters would have a better ROI, but I suspect not.

Last time around I was really bad with social networking: the timing really worked against me, releasing right into my PhD defense, and then having Blueberry. This time I will try to distribute sample chapters and deeper discussions as guest posts on other blogs (if they’ll have me). Of course the problem there is that I might be hitting the wrong audience: it’s the people who aren’t reading personal finance/investing blogs who need the book the most. Good reviews on Amazon help, and I will plead with people to fill those out (their honest opinions — I’m not down for astroturfing). But if readers who liked it are already not telling their friends, going to the effort of writing a review may be out of the question.

So I have to admit it: I am not good at marketing. I have no idea what else to do. Suggestions, blogosphere?

Help me Obi-Wan Kenobi, you’re my only hope.

* — True story, nearly no hyperbole (at least, not in the retelling).

To Put It Another Way

September 25th, 2014 by Potato

Once again I saw the “but if I buy a house I get something back. If I rent I get nothing back. Even a small return is better than zero…” trope about renting vs. buying. This time I answered it slightly differently, and maybe this explanation will stick:

You have to look at the whole picture.

Give me $10. I will buy you a bag of chips and give you $2 back. Hey, a small return and a bag of chips, that’s good, right? But if you can just buy the bag of chips for $5 you’re better off — you can hold on to $5 out of your $10, rather than just $2. There’s no “return” in the second case, but you put out less to begin with. In both cases you get delicious chips.

So it is with housing. The key thing to appreciate is that all discussions of “building equity” and what-not are distractions: at the end of the day, living somewhere is going to cost you money. This is where the details matter: how much money for each option? If the total cost of owning (interest/opportunity cost, transaction costs, upkeep, insurance, property taxes) is more than the total cost of renting (rent, tenant’s insurance) for the same place and you invest the difference, you’ll do better renting.

Cover Design Update

September 24th, 2014 by Potato

I had originally scheduled a minor reveal post today where I was going to tell you all the amazing title of my amazing new book and provide an amazing (-ly short, for me) synopsis, to start building something I’m told is called “buzz.” Big with bees, I hear. Anyway, in talking with some people about that the point was raised that maybe I should keep totally silent until the book is actually available for pre-order (rather than the pre-pre-order state it’s in now where you email me and I add a mark to my tally to guess how big to make the initial print run). I think I will explode if I wait that long, so I’ll probably just end up publishing that reveal post tomorrow anyway.

I got the first drafts of the cover concepts back from my artist today and I’m quite impressed. There was a concept that some people liked because it really said “this book is about doing stuff with money.” But it was the first one I threw out because it was so generic. The one I immediately decided was the one is a bit different, which I hope means that it will stand out on the shelf and make people pick it up. Hopefully only another week or so then until I can swap out the teaser image on the right with the actual cover (unless I listen to reason and wait until pre-orders open).

I still haven’t set a firm date to take PSGtDIYI out of publication yet. Expect that it will happen suddenly on the same day that (firm) pre-orders open for the new book.

I’ve had to enter pricing information to get my ISBN* and UPC code, which means I had to decide on pricing without having a proper public hand-wringing about it. I can still change it, but I think I’ve settled on going a little bit cheaper than most of the books out there (which have a list price of $19.95 but actually sell in the mid-high teens). I went with what looks like an odd price, so that with HST (5% on books) it will come out to an even dollar amount if you’re paying cash. I don’t really know how much something like that might phase people (or please them). I also don’t know whether being a few dollars under the $19.95 cluster is attractive or gives off a “stinky kind of cheap” aura.

* I have an ISBN assigned. Several, actually! Squee!

We Have TFSAs Now: Lose the HBP

September 18th, 2014 by Potato

A little while ago Rob Carrick idly wondered on his facebook page/discussion group if the home buyer’s plan (HBP) was a good idea. In case you’re not aware, the HBP is one of the few ways you can take money out of your RRSP without paying tax on it: you can pull up to $25,000 out as a first-time buyer, and repay it over the next 15 years. The HBP primarily accomplishes two things.

1. It lets people contribute to their long-term (retirement) savings with an “out” to use those funds for a down payment on a house/condo. This way they can save for the future without having to plan what will be house funds and what will be retirement funds.

2. It lets people get a tax refund on their down payment that they can also use on the house right away, effectively borrowing from their future selves. In the short term, it’s an incentive to buy.

On top of this, it has a psychological effect: home ownership and post-secondary education are the only sanctioned reasons for borrowing from your RRSP. Add how irrational people can be about taxes and tax deductions, and it’s a bit of a sacred cow. In the right light (octarine?) it looks like the government encouraging buyers to reach for as much real estate as they can, using everything at their disposal (including their RRSP).

With TFSAs in place now though the first point is well taken care of by that tax shelter: you can easily throw all your long-term savings in there as a young person, and if you need to raid them for a down payment (or whatever) then you can, even in excess of $25,000. Plus it’s already set up to be indexed to inflation so we won’t have to worry about future whining that the HBP isn’t big enough. As for point two, I really don’t think we need any more tax incentives or holiness attached to housing, so doing away with the HBP in favour of encouraging TFSA use would suit my politics just fine.

To be fair, this may need a few years for transition, and would present a bit of a savings conundrum to people who get employer RRSP top-ups, but I find it hard to feel that’s a major flaw in my plan. Let’s simplify the RRSP that one extra step, and phase out the HBP.

Potato’s Third Law (of Finance)

September 18th, 2014 by Potato

Clarke’s third law:

Any sufficiently advanced technology is indistinguishable from magic.

Potato’s Third Law (of Finance):

Any sufficiently complicated analysis is indistinguishable from magic.

A few months ago, Brad Lamb posted this inane thing, suggesting that buying real estate in a highly leveraged way beat out investing in any kind of normal way because, with an average 5.5% return over 30 years and lots of leverage, you’d make scads and scads of money. Of course, that’s clearly a biased and overly simplistic analysis from a source that is, well, you get it. For instance, one important consideration in using massive amounts of leverage (95% in his example) is the cost to borrow. And if you look it up, over those same years the (simple) average mortgage rate was 9% — blowing the 5.5% appreciation out of the water.

Obviously there are lot more factors at play than just appreciation, but many people will have trouble following the red lady as these condo kings play their three-card Monte.

Similarly, Melissa Leong recently wrote about Sean Cooper’s quest to save at an incredible rate and pay off his mortgage crazy early. While her article was very fair and level-headed, someone at the National Post decided to put this sensationalist caption to the preview: “Sean Cooper’s secret: He rents main floor of his house, while living in the basement and bikes and uses TTC instead of a car.” [emphasis mine]. While only part of the numbers are shown, if you work the math and make reasonable assumptions you get a fairly unsurprising result: he ends up paying about $800-1000/mo to live in the basement of his house. Which is what a basement apartment including utilities costs in that part of Toronto. Renting out the main floor of his house is no secret at all — the progress he’s making is solely due to the other insanely frugal and hard-working things he does, like biking everywhere and avoiding taxis or car ownership, working multiple jobs 7 days a week, and reusing everything to the maximum. The fact that he’s renting out part of his house is pretty much irrelevant to the story, but it looks like magic because it’s complicated and because for some reason being a landlord is high-status. Indeed, given the timeframes he’s been working under, he would have done much better doing all the hard working and frugal things he’s doing but plowing his money into index funds.

When there are a lot of factors in the analysis people just don’t want to deal with it. It all bleeds together and acts just like magic, so it becomes hard to critically assess what’s being presented. This happens a bit with a few topics in finance like investing, but it seems to be most prevalent — and most exploited — in real estate.

Take for example the terrible condo ads around Toronto that should be banned for what they try to get away with in the condos=magic department. Here’s a recent collection tweeted by Ben Rabidoux:

To pick one, the Thompson Residences in case you can’t read the image, it claims an 18.6% return on investment (such precision!) with no attempt to back it up (the fine text the asterisk leads you towards just says something about the parties not warranting or representing any of the figures). Another (Axiom) also claims 18.6% returns (they must have done some market research to show that this completely made-up number has some truthiness and feels more correct and gets people to buy than some other random number), this time on the unlevered condo. Of course they don’t provide the full details, just assuming that you’ll rent the place for $2355/mo (such precision — also that gets you a 3-bedroom detached house in many parts of Toronto, but sure, let’s just go along and assume a 1-bedroom downtown-ish is worth that because… George Brown?), and somehow make $685 in positive cashflow and $607 in principal repayment. So after interest (at just 3%) you’ll only have $227/mo for tax, maintenance, insurance, and condo fees (yes, that’s totally reasonable — oh wait, no maintenance fees for a year, of course that’s a representative calculation then). But then you take those phoney rent profits and add it to their phoney price gains ($58,993 — yes, also down to the dollar) and you know what you get? 17.8%. Not 18.6% like they say.

Clearly these ads are not targeted at the careful, numerate buyer — they can’t even be bothered to make their fake numbers internally consistent.

Where was I? Right, magic. Well, there’s clearly some smoke and mirrors going on in those ads.

Tater’s Takes: Tax Refunds Are Not Windfalls

September 11th, 2014 by Potato

I haven’t had a Tater’s Takes round-up post in approximately forever. Preamble: early summer was crazy at work, so it was good that I finished the draft of my book in the spring so it could sit with the editors over that time. Several people now have copies in their hot little hands and are providing great feedback so I can make one last round of polishing before I start getting proofs made up. I’m getting super excited for the book. I’ve put a tonne of effort into it (way, way more than I expected when I thought I’d just make a PSGtDIYI 2nd edition) and I think it’s shining through in the manuscripts. Most people who haven’t gone completely silent have praised the initial copies, particularly novices to finance (the target audience). There’s still almost two months to go before I run out the clock on the window to hear back from publishers, and at this point I almost want to get rejected because it’s just so close to being ready to go in the self-published route that it would hurt to have to pause to work out the details with a traditional publisher.

Blueberry is (as every proud daddy will say, I’m sure) uncanny smart sometimes. Like most toddlers, she has become attached to a blanket as her “lovie”. We’ve heard the horror stories of kids who lost their lovies or those that get disgusting because it’s hard to separate them long enough from the child to wash, and Wayfare planned in advance. We bought multiple copies of the blanket in question, and have kept them in rotation so there’s always a clean one ready and so that they all have the same degree of wear. These blankets are identical in every way, right down to their electrons sharing the same spin states. So we were caught completely off guard when Wayfare surreptitiously did the blankie swap for laundry and Blueberry instantly noticed and freaked out. How could she tell? How could she tell so quickly and decisively? Baby genius, that’s the only answer.

Ok, links.

First up is yours truly, scraping the bottom of the barrel for active investing ideas. I hardly post at all on that topic, and considering I’ve got a book on how easy index investing can be coming up it was best to shunt it to another venue. Nelson was kind enough to host this post on HNZ over at Financial Uproar.

I’ve just discovered Steve at Kapitalust. I’d suggest starting with this recent post on the intersection of ethics and investing.

Sandi’s back! Or semi-back, as someone else takes over half-way through.

Robb at B&E preaches about the inevitability of changes to embedded commissions for advisors in Canada.

Michael James has a new twist on comparing car salescritters to mutual fund salescritters and why embedded commissions make more sense for one than the other.

Oh, so this is public now.

Dan at OBFW reviews a new book (not mine, despite what you may think when you see the title — I’ll unveil the title of mine in just a few more weeks, be patient kids) and raises an interesting question: “Would you rather get a $1,000 windfall at age 27 when you are trying to scrape together a down payment for a house or a $1,300 windfall at age 70 when you have close to $1 million in savings?” in suggesting that young people use their RRSPs over TFSAs (and spend the refund).

I think that’s unfortunate framing. A tax refund on an RRSP contribution is not a “windfall” — it’s a deferral of a government obligation. Michael James puts it best when it calls it the government’s share of your RRSP. Of course the short answer is that if you really need the money to buy a car or pay down debt then you should just use the money for that rather than investing it and then redirecting a part back towards the more urgent need in a roundabout way that involves filing paperwork with a large government agency. But let’s do the math on this suggestion:

Let’s say you scrape together $1k to invest while you’re in the 20% tax bracket at 27, and expect to end up withdrawing in retirement at age 70 in the 31% tax bracket. We’ll use 6% real returns. If you suddenly realize, no, you need $200 of that back to pay down some debt you forgot about or to buy something shiny, then you could either put just $800 in your TFSA, or contribute $1k to your RRSP and spend the $200 refund.

If you just trusted your original decision to invest $1000 in your TFSA, you’d have $12.3k to spend in retirement. But to be more fair, the invest-$800-in-your-TFSA scenario would leave you with $9800 to spend at age 70. If you put the $1000 in your RRSP and got a $200 refund to spend on stuff then you’d only have $8453 to spend after the CRA took their cut in retirement. Spending the government’s share and mistaking the TFSA vs RRSP issue adds up to a much bigger deal than just $1000 when you’re young or $1300 when you need it less — you could spend the same “windfall” amount on whatever necessities you have when you’re young in that case, still use your TFSA, and come out way ahead.

If you only decided to spend the refund because it came months later and you were weak (and you didn’t get commiserate value from the dollars spent), then picking the RRSP over $1k in the TFSA would be like borrowing $200 from your future self and paying an interest rate of nearly 7%. But, maybe spending $200 now is more important than spending $3847 when you’re 70 and don’t need it. Of course that logic of “X now is more important than Y later” can lead to a lot of debt if you don’t put some reasonable limit on it.

Nelson also posted about why he prefers the RRSP to the TFSA. I left a weak, off-the-cuff comment about why I still like the TFSA. One other point that came to me when re-reading it is the issue of the refund timing: if you run the math, assuming you’ll be in the same tax bracket before and after retirement then the two shelters come out neck-and-neck in terms of outcomes. If you end up in a lower tax bracket the RRSP provides an advantage; higher and the TFSA will win out. However, the canonical comparison assumes you invest with pre-tax money and avoid withholding (or have the funds available to invest the refund in advance). In practice not only do people run the risk of squandering the refund, it also tends to come later, so the TFSA gets a tiny, miniscule head start on compounding (when looking at it from multiple decades in the future). Anyway, nitpicky.

Use RRSP with DB Pension?

September 9th, 2014 by Potato

Over on the twitter, people wondered whether to contribute to an RRSP if they have a defined benefit pension plan. The answer depends on a few factors, chief amongst them your expected tax rate in retirement versus your tax rate now (or in the near future if you choose to contribute now but defer the deduction for a while). Other factors can include your situation and plans — if there’s a decent chance you’ll need the money before retirement, it may be best to keep it in a non-registered account until you’re sure you can lock it up.

The short answer is easy though: most of the time an RRSP is better than investing in a non-registered account, even if you have a DB pension. You can think of it like this: you have a pension adjustment if you’re in a DB plan, so you likely only have a bit of RRSP room, with the rest being used by your pension. If you had no pension and lots of room, would you use all of it or only 80%? Maybe you’d be in a case where only using a bit made sense, but likely you’d use it all if you could.

Really the only clear case where you should not use your RRSP is if you expect to be on GIS in your old age (but in that case it’s not likely that you have a job that’s offering a DB pension).

The easy case is when your tax rate in your earning (and saving) years is higher or equal to your tax rate in retirement: the RRSP will make sense (assuming you invest the refund or would invest less if you were using a non-registered account). Indeed, if you do invest the refund the RRSP will beat out the TFSA in terms of returns for the case where your tax rate in your savings years is higher than in retirement.




The harder case is to construct a scenario where your tax rate in retirement is higher in retirement than in your working years. If you’re particularly high in the income spectrum then you could have OAS clawbacks, effectively a 15% surtax on retirement incomes over $71k — which if you’re using a typical DB replacement of 70% means you’d be making over $100k in your working years (over $115k in DB income — say $165k in your working years — and it won’t matter anyway). The most likely case for higher tax rates in retirement is the least predictable one: where your inflation-adjusted income stays the same, but the government of the future has raised tax rates. It’s an analysis paralysis black hole to try to worry about deviations too far from the present set of rules. You could be higher than you are today if you make a lot more later in your career, but then if you expect to move up a tax bracket or two you can still contribute to your RRSP and defer taking the deduction. Still, the answer is not as simple as “skip the RRSP if your tax rate in retirement is higher.”

Even if your tax rate will be higher later, the RRSP can still beat out a non-registered account by allowing for tax-free compounding and easing the record-keeping and reporting burden of investing. The tax-free compounding benefit doesn’t sound that spectacular, but bear in mind that after the first jump the marginal tax brackets in Canada increase fairly shallowly. For instance in Ontario the difference between earning $75k and $90k is only 6%, and that’s made up of a federal 4% jump and provincial 2% increase at similar but not quite identical break points, so you could be “higher” later but have an even smaller difference of maybe just 2%. Would tax-free compounding be worth that?

It’s tough to say because the drag from taxes is not precise, and you can defer some capital gains into retirement, but let’s estimate it: assume you have an 8% nominal return (note that taxes are on nominal returns rather than real returns). Assume that your employment marginal tax rate is 31%, and that through the magic of capital gains partial inclusion, the dividend tax credit, and handwaving, your tax burden on those gains is 12% per year (taking a rate below the half-way mark to try to assume some benefit of capital gains deferral). Then you could invest $10,000 after tax in a non-registered account, earn 8% nominally, and pay $96 in tax the first year, or put the $14,493 pre-tax* into an RRSP, and earn 8% tax-free. After 10 years you’d have $19,745 in your non-registered account versus $31,289 in your RRSP. The tax drag would mean that your tax rate could be as high as 37% after 10 years — 6% higher than our starting tax rate or a full federal + Ontario tax bracket move — and the RRSP would still roughly break even. As time wears on so does the non-registered tax drag — after 28 years in this example the tax-free compounding benefit would offset being hit with OAS clawbacks.

I’m not sure what the correct estimate of the non-registered tax drag would be, but in this example I’m neglecting any tax on deferred capital gains which would further improve the outcome for the RRSP case. I’d ballpark it as somewhere between 1/4 and 1/2 of your marginal tax rate, and likely closer to the high end of that.

So yes, there is a very good chance that investing in an RRSP will beat out investing in a non-registered account, even if you move up by a tax bracket over time or face OAS clawbacks.

Basically:

  • If you’re really low income, where you expect to get GIS in retirement, then avoid your RRSP. Invest in a TFSA, and if you manage to have more to invest than your TFSA contribution room, invest in a non-registered account.
  • If you’ll be in the same or a lower tax bracket in retirement, then definitely maximize your RRSP! Tax arbitrage FTW! Just remember to invest the refund too, where you can.
  • If you’ll be in a higher tax bracket then it may still be worth it:
  • If you’ll be just one bracket higher, it will quite likely work out better with an RRSP due to the non-registered tax drag.
  • If you’re in the OAS clawback range (expected retirement income of ~$71k-$115k in today’s dollars) then consider it carefully, but enough time and non-registered tax drag may still make it worthwhile.

I’ll finish by noting that my rule-of-thumb is simply “TFSA first”. For many the RRSP will come out mathematically optimal (note that the TFSA gets the same benefit of tax-free compounding discussed here), as many people can expect to end up in a lower average tax bracket in retirement. However, the TFSA is more flexible, better for lower-earning people, and moreover is easier to plan around with set contribution limits by year and no pension adjustments, and higher income people can usually find the funds to contribute to both. Mostly though it’s the gap between theory and practice that makes me push the TFSA: most people do not put pre-tax money in their RRSPs (or invest the refunds) — they invest what they have on hand at the time they decide it’s investing day, and then if a refund comes in they spend it. Plus if you figure out later on that an RRSP is better for you, you can easily withdraw from your TFSA and start catching up on your RRSP — if you don’t know any better, the TFSA is a great place to start. Once your TFSA is full, moving on to RRSP next (over non-registered makes sense)**.

Finally, a good related post at Michael James on Money that I couldn’t find a place to link to above.

* - remember that the 31% tax rate is on the pre-tax amount, so the RRSP will have more than $13,100 to invest, but this may come as $13,100 in the first year, then a refund on contributing the refund in a following year, repeating. Or you could fill out the paperwork to get pre-tax money into your RRSP by avoiding tax deductions in the first place.
** - which doesn’t mention the RESP. That depends on your priorities and view towards paying for your kids, but free CESG money is hard to beat so it often goes even ahead of the TFSA.

Back-of-the-Envelope: Motion Sensors

September 8th, 2014 by Potato

In the name of efficiency, many places are moving towards using motion detectors to control the lights, which can be annoying when the decision circuits decide the room is empty and turn the lights off on you. On the whole I find sensor-controlled lights more of an inconvenience than a labour saver. Still, if the lights are off more that’s going to save power. Advances in lighting efficiency means it’s not quite as bad as it used to be to leave the lights on, but unless there’s a next-generation LED technology coming, turning them off when you’re not in the room is still going to be a necessity as always-on lighting just isn’t realistic.

However, motion detection isn’t free, either: the sensor uses some electricity, and of course has some capital costs. So the question is how bad do you have to be at turning off the lights for a motion-controlled light system to make sense?

Doing some brief research (I googled it), the sensor is not energetically expensive: drawing roughly half a Watt, that’s only 4 kWh/year. If the sensor is controlling four 100 W incandescents or eight 50 W halogens, that’s only ten hours of accidentally leaving the lights on, less if it’s an even larger room or hallway. Of course with lighting getting more efficient, even setting aside LEDs and using four CFLs of 13 W each, it would take 77 hours of accidental usage to break even, or about 12 minutes per day. And you have to be especially negligent to make it worthwhile to put a sensor on a circuit with only one or two bulbs.

And on the flip side, sensors can lead to more light usage if you rely on the timer to turn the lights off rather than turning them off yourself. If you leave a room long enough for the lights to turn off say 3 times per day, and each time the lights burn for 2 minutes longer than they would have if you just hit the switch on the way out, then that’s an extra 36.5 hours of light caused by the switch. More if there’s more in-and-out traffic through the area, less for more rarely visited spots.

It might be because I’ve got investments on the mind, but this sounds like it’s going to shape up to be an analysis focused on risk: if the room is a place you go to infrequently with your hands full (so less likely to turn the lights off, and more likely to have them burn for a long time if your forget), with many high-consumption lights, then the risk of having the lights burning all weekend may outweigh the drain (and capital cost) of the sensor.

There are some other benefits to motion sensor controlled lights, such as infection control. There are also drawbacks, such as the existential crisis that happens every time the sensor fails to see you: are you a ghost and just don’t realize it yet, or is the sensor on the fritz?; and DEAR GOD TURN THE LIGHTS ON ALREADY I’M JUST TRYING TO POOP AND WHY IS IT DARK?

In the end though it doesn’t look like we’re talking about large sums of money either way. 4 kWh/yr will work out to about a dollar in electricity, and the sensor-powered light switches are only a few dollars more than a regular one. For your own private dwelling it may be a toss-up, but for a lightly used commercial washroom the math may make more sense, when the lights could be left on unnecessarily for hours every day. Which is a shame, because those are the same places where the malfunctions are most annoying.

Pizza Math

September 2nd, 2014 by Potato

A reader requested this a long time ago, sorry for taking so long Ben!

The age-old question: is the medium the better deal, or the large? The medium may be cheaper per slice, but each slice on the large is bigger…

The math to figure this out is not hugely complicated, but it’s just a bit more than you might be able to do in your head or with a smartphone while you’re hungry and staring at a menu board. What we’re interested in is the area of pizza that you get per dollar. The area of a circle is simply pi * r2. Pizzas are sized by their diameter (double the radius). However, there are no points for crust (”pizza bones”), so we’ll subtract 1″ from each diameter (for a typical 0.5″ of crust on each side of the line through the circle) when computing the area factor. Because we’re really just interested in the relative value we don’t necessarily need to do the division by two or multiplication by pi — the pizza value will scale with the square of the adjusted diameter — unless we’re comparing to a square pizza. While some pizza places use their own wacky sizes, or have irregular hand-shaped crusts, most places have settled on standard sizes. I’ve listed the rounder area factors and actual edible areas below:

Small (nominally 10″): Usable diameter of 9″, area factor is 81 (edible area of 63.6 sq. in.).
Medium (nominally 12″): area factor is 121 ( 95 sq. in.).
Large (nominally 14″): area factor is 169 (132 sq. in.).
Extra Large (nominally 18″): area factor is 289 (227 sq. in.).
(note that Pizza Pizza and some other stores have 16″ extra larges)

Square pizzas: most often encountered with party sized pizzas. In this case to make a true comparison you would need the circular pizzas area in square inches. For a 15×21″ (nominal) party pizza, there are 280 sq. in. of edible pizza. Converting into “area factor” above, that would be 356.

To put this into practice then requires a division step with the price. You can divide the price by the area factor to get a price per unit area — then lower is better. However, because pizzas are often priced near $10 or $20, the inverse may be more convenient to work with — pizza units per dollar — in which case the higher the number the better value. For example, if a large is on for $10, the pizza per dollar is 169/$10 = 16.9. If the medium is $8, that’s 121/8 = 15.1; if the party size is $20 that would come to 356/20 = 17.8. In that case the bigger you go, the better your value.

For your convenience, I made a reference card for your wallet. (Be sure to select “actual size” when printing)

I’ll note that dollar per unit pizza should be the preferred unit/method if you want to look at how the value difference scales across pie sizes rather than just which is larger — analogous to the L/100 km measurement system vs MPG issues.