Nothing important

Wow, it's been a while since my last post. I guess it's a combination of being busy at work and August having been a pretty uneventful month. The most exciting thing that's happened is me trying to find half-price meatballs on sale (click on picture for some more recent pictures taken around home). It's been cloudy or rainy for at least 5 days a week all month, so I haven't gotten out much. The days are definitely getting shorter, too - it used to be broad daylight at 10pm, but now it's pitch dark after 9. It's also hard to believe that there's only 4 weeks of work left, and I haven't done half of what I aimed to do. No matter, I still learned some very nifty tricks working with Excel and VBA. I'm actually leaving my collegues a "software package" (probably a very inappropriate use of the term) consisting of an Excel add-in that will automate a lot of very tedious and high-volume manual work. I just hope it doesn't become obsolete from changing requirements 2 weeks after I leave. If nothing else, at least it made my own work easier. Also, Brian is coming this Friday to get a taste of Stockholm for five days (I hope the weather will cooperate), and next Wednesday we'll be off together to see Kari in Vienna for another five days. That should enough excitement to break this month's dry spell. After that, I'll have only another two more weeks of work! Time is really just wizzing by.

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Back to the mundane

Perhaps you've noticed already, but I'll remember Stockholm by its snails. There's the huge white type, and there's the colourful small type that, as I found out today, gather in groups and either eat or mourn the crushed white types. This one is headed for one such party. Click on it for more.

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Mortgages - part 2

Ok, so last week I made mention of how rent paid today is actually buying valuable time to increase the size of a down payment. But how to quantify this? Beware, the answer might only appeal to those with a bit of finance background or who were forced to take a course taught by a certain jolly accountant with an interesting sense of humor. First, you must research and decide the following variables:

• Q, Current savings – size of your savings today (or whatever time you consider time zero)
• r, Savings rate – rate at which your savings earn interest
• S, Annual savings before rent – how much you can put in the bank each year after expenses but before rent
• R, Annual rent – how much you expect to pay in rent before you buy a house (can be zero)
• P, Price of house today – the current price of the type of house you’d like to buy
• p, Price inflation rate – percentage the price is expected to go up each year
• m, Mortgage rate – the interest rate the bank charges you for a mortgage (assume fixed)
• M, Annual mortgage payment – how much you’d be willing to repay each year

To take into account the time value of money, we’re going to find the present value (with respect to now, or time zero) of the sum of rent, down payment, plus mortgage payments from now until when your mortgage is repaid, as a function of x, the time in years at which you buy your house. Note that the discount rate represents how much interest you’re missing out on if you spend your money instead of saving it, so for the conversion factors the discount rate will be r (and not m, which is another interest rate for another purpose).

When you buy your house at year x, you have paid an annual rent of R for x years. This amounts to a present value of R*(p/a, r, x). This is the cost of rent.

When you buy your house at year x, you would have saved up Q*(f/p, r, x)+S*(f/a, r, x). This amounts to a present value of Q+S*(p/a, r, x). This is the cost of the down payment. When you buy your house at year x, the price of the house would have risen to P*(1+p)^x, while your savings would have grown to Q*(f/p, r, x)+S*(f/a, r, x), both values with respect to year x (not today). That means you will have to borrow B=P*(1+p)^x-[Q*(f/p, r, x)+S*(f/a, r, x)] from the bank. Given that we’ll pay back M dollars a year and the bank charges an interest rate of m, what’s the present value of all your payments? To answer that, we must first find out how long the payments will last. Let’s jump to year x and think about present value with respect to that time for a moment. Consider that the amount you borrowed, B, is precisely the (hypothetical) present value of all your payments at a discount rate of m. To find out y, how many years it will take to repay the mortgage, we must solve the equation B=M*(p/a, m, y) for the value of y. As it turns out, y=ln[M/(M-B*m)]/ln(1+m). The constraint of the logarithm states that M must be greater than B*m, which makes sense, because it says your annual payment should be at least as much as the annual interest, or else you’ll never pay it all off. Ok, so this means that, with respect to year x, the present value (with the real discount rate of r) of all your mortgage payments will be M*(p/a, r, y). If we convert this to the present value with respect to time zero, then we apply a further factor of (p/f, r, x). So the total cost of buying a house in year x, in present value with respect to today, is R*(p/a, r, x)+Q+S*(p/a, r, x)+M*(p/a, r, y)*(p/f, r, x), where y=ln[M/(M-B*m)]/ln(1+m), and B=P*(1+p)^x-[Q*(f/p, r, x)+S*(f/a, r, x)] Now this isn’t an easily differentiable function with respect to x, so the easiest thing to do is to enter the formula into Excel and let it show you what the present value is for x equals a variety of values, and find the x for which total present value cost is minimized. For example, let’s say I want to aim for a type of house that costs $400k today, and rises in price by 7% each year. My annual rent in the mean time is $10k, my annual savings is $50k (before rent), the savings rate is 6%, the mortgage rate is 10%, and I’m willing to pay all $50k of savings into mortgage payments after I take a mortgage. My formula tells me that I best buy a house after 3 years of renting, at a present value total cost (rent plus mortgage) of $516k. If I were to buy the house today because someone told me that paying rent is like burning money, then the present value cost of the house would be $522k. So, by staying put in my apartment over 3 years, I saved $6K PV by the end of it all. Remember, that's $6K in present value, which, at 6% savings, will grow to $18K by the time I repaided the entire mortgage.

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Some new pictures

Pictures of famous buildings and other tourist sites are great, but they don't really show my daily life for what it is (i.e., always trying hard to not crush snails). Now that there are less than 2 months before I head back to Toronto, I've decided to keep my camera on me as much as possible. I'm going to add these into a single Flickr set, sorted from most recent to oldest, and I'll be sure to announce significant additions. I just made some additions today. Go take a look! Oh yea, my new roommate seems like a nice guy, although I haven't had the chance to talk to him much yet.

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My new room

My new roommate (for back story see here and here) will be moving in either tomorrow or Monday, so I'm slowly moving my things into my new room. I get to enjoy a different view (this time out of the front of the house), a bigger desk (exactly the same Ikea desk as I had in Toronto), and a couch for a bed (which I just tested with an afternoon nap; verdict - 4 hour nap!).

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A consideration of mortgages

When work becomes a bit dry, I let my brain wander onto other things... two weeks ago it was bicycles and monorails. Today: It might be that time in life for some of us (maybe not for you grad students) to consider buying a house and settling down. Natural questions arise, such as, "how much can I afford on my current salary?" and "how long should I take to pay it back?" Mortgage "calculators" offered by banks such as TD are often oversimplifying the problem, and only shed light on the relationship between monthly payment, principle, interest rate and payment term. There are far more factors involved than just those. Anyone who tells you "every dollar you pay in rent is money thrown down a well" is either a loan officer, a real estate agent, or an miseducated (but well-intentioned) parent; none speaks the truth. If you're planning on buying a house in a few years, rent you're paying now is buying you time to save up for a big enough down payment to save on interest from a mortgage. Provided you have a job. Let's say you're currently renting and can put $20k into a savings account each year. And let's say you plan on one day taking up a 15 year mortgage at 10%. It might occur to you that for each additional $20k (a single year's savings) you put into a down payment, you will save $63.5k in interest by the end of your 15 year term (because you didn't have to borrow an extra $20k for 15 years at 10%). Suddenly that $500 a month rent seems worth it, right? Even that's oversimplifying it. Your savings is generating interest of its own at 4% (or if you're smart and have a good investment, 9%). The type of house you want to buy is perhaps growing in price at 5% a year. Maybe your rent is actually zero because you live with your parents. For each additional $20k you put into a down payment, your payment term decreases (for the same monthly payment), which decreases the savings on interest caused by the next 20k you put in. So bottom line: when's the best time to buy that house? Finding no easy answer on the internet (or maybe I didn't look hard enough), I set out to answer that question on my own. I haven't quite worked out the kinks in my formula yet, and this post is getting too big, so stay tuned for the conclusion.

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Paris adventures

I have finally sorted through all my Paris pictures. I try to give each photo a bit of special attention, and at least half of them are stitched from more than one shot (blame the horribly long focal length of my camera lens). It takes a bit of time, but I try to make my photos a happy medium between those that are purely artistic and those that are purely practical. I'm starting to think photos of fun times aren't as fun without showing myself doing something fun, but that's what you get for travelling alone. I've created two sets:

• The (mostly boring but sometimes amusing) shots of, and out of, my various forms of transportation between home and Paris;
• The (more interesting) shots of my stay in Paris itself.

The uploading process is a pain with the slow internet, and is only less than half done. Check back soon! Hopefully I'll compose a couple of videos too.

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Got pissed too soon

In my own defence, I honestly didn't think I'd see Bertil (my very sweet landlord) until "eviction day" a week from now. I haven't seen him for two or three weeks. And in my own defence, the threat of calling that new apartment a home was a pretty hard hit. However, my agitation turned out to be premature. Bertil came home just now (only for about an hour before leaving again), and said that it would be no problem if I lived on the couch in his study for the remaining two months. That really made my day, week, month, and possibly year. So, the threat of a move has been lifted, and I get to live in this idyllic little suburb for another two months. I really wish I asked him about this the last time I saw him, but (again) in my own defence, I had no idea it was necessary.

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Got excited too soon

Well, the Pride Parade got rained on. It wasn't pouring rain, but the type that sticks around for the whole day. The Parade was still festive with (as expected) lots of skin, but it wasn't as fun as it could have been on a sunny day. I think the real surprise was the new apartment, which turned out to be a 70 square foot room with a stained couch and a rickety table, on which stood a microwave and a hot plate. The bathroom was no bigger than a powder room, except there was a spray nozzle from the sink I'm supposed to take showers from. The "landlord" lived in the same apartment, which strangely has both a separate entrance and a locked door directly to this room. He was full of tattoos and his gaze suggested he might have been on a bit of an influence. The last thing he said to me was "if anyone asks, tell them we're friends" in broken English. As we departed, I told the nice IAESTE Stockholm member who accompanied me that my minimum standards are a teeny bit higher for 3500kr a month (about $600 CAD). So, the alternatives would be to stay at my current place in an extra room for a while longer (I haven't seen my landlord in weeks, but he's a very nice man who I really don't expect to throw me on the curb), and in the long term, get a private room in a hostel with half the expense covered by IAESTE (or so I'm told). I'm glad I didn't buy a bus pass. My only regret is I didn't take some pictures before I left, since I think this was a very interesting highlight in my experience in Sweden so far. Regardless, suddenly I feel a lot warmer and fuzzier about my current place.

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The stars are out - the summer is fleeting

In most of June and July, nights are filled twighlight. The sun barely sets before it rises again. I haven't been up this late in Stockholm for some 2 weeks, but just now, I noticed that the night is totally dark and the stars are visible for the first time this summer. To the locals, this might be a stark reminder that short, cold winter days are approaching. Thank goodness I'll be out of here by then.

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Two things to look forward to

• I'm getting the keys to my new apartment this Saturday. It's about 30 minutes away from work by transit, which isn't great, but I'm relieved that a place has been found. I can stay at my current place for another week after that, which means I'll have plenty of time to pack and move. I actually don't know any details about what this place looks like and whether I'll have roommates, so, as a continuate of a recurring theme, we'll see when we get there.
• The Europride parade is this Saturday, as a part of a week-long Pride festival. Apparently Stockholm hosts its own festival and parade each year, but this year the Europride rotation is here, which will make this the largest event ever. Should be a sight to see!

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