Brainteaser - NY Tube
Hi all,
I'm preparing the following brainteaser but fail to come up with a clever answer
Please feel free to share any thoughts / inputs, that would be really appreciated
The New York City subway currently costs $2.50 to ride one way. Pretend that tomorrow, the cost is going to increase to $3.00. Assuming you can lock in the $2.50 rate in the future by paying for the future rides now, how many coins would you purchase? What are the key considerations to make?
Thanks a lot!
I'd buy enough for however many years I'd see myself working in the city. assuming you go out on weekends, thats atleast 14 journeys you'd make a week. Multiplied by how many weeks youd expect to be in city (i.e. not on holiday else where). Then I'd also consider buying same for partner if i had one. Then finally i'd consider buying them simply for resale purposes. Chances are that they wouldnt stay 3$ for ever and would eventually increase to 4$ etc and at that point you could start getting a nice return on the ones you have by reselling them (e.g. for 3$ etc). Obviously would also weigh this up against alternative forms of investment available etc.
I think the key to this problem is considering the discount rate.
Tomorrow the $3 you would spend is approximately equal to $3 today (because you're only discounting 1 day), which is obviously greater than $2.50 today, so it makes sense to buy tomorrow's ticket today.
However, consider 10 years from now. $3 in 10 years is worth much less than $2.50 today due to the discount rate (if it's not, you can substitute 50 or 100 years). Therefore it makes more sense to buy the $3 ticket in 10 years than it does to buy a $2.50 ticket today.
Therefore at some point between tomorrow and 10 years from now, $3 at that date is equal to $2.50 today. Your optimal choice is to buy as many tickets as you plan to use up to that date. The math is basic algebra and should be pretty easy to walk through.
This.
Only other I'd add is what if a) price of ticket decreases in future (yes, highly unlikely) or b) another method of transport is introduced or improved ($2 Uber rides, cheap bike rentals, etc) that could put a dent to the value of the future rides that you've bought, so you'd do impair future ticket values hence decreasing the equiv. discount rate less / $ of tickets you buy today.
delete
Yes agree, can't think of anything else.
Thanks
Can you resell them in this scenario?
This is more like an MBB case question than a brainteaser. It brings me back to the interviews...
Literally, there are so many ways to go with this. There is no right answer. Just be logical in your thought process (while also throwing shit at the wall and hoping it sticks), and you'll be fine.
Assuming no resale, say your discount rate is the historical returns of the S&P 500 (~7%). In other words, you believe you are likely to, on average, achieve 7% from the market, so you want to find out the quantity you would buy before you're likely making a bad investment decision by having too much money wrapped up in the tickets.
Therefore, how many years would it take for that $2.50 to be equal to $3 at that rate?
FV / (1 + r)^t = PV
3 / (1 + .07)^t = 2.5 3 / 2.5 = 1.2 = 1.07^t log 1.2 / log 1.07 = t
t = 2.69. So buy however many you would need to last for the next 2.69 years, after that it's not worth it.
Very good perspective, thank you for sharing
You seem to have found the answer you were looking for on this thread but since you're preparing the brainteaser, just wanted to bring up that subway fare in NYC is $2.75 one way right now (really not trying to be rude, just want your brainteaser to be accurate).
Well the answer, as the consensus has shown, is to buy as many as you can. But there are somethings to consider beforehand and that is risk. My time trading has shown just how much we tend to jump the gun so what are these ambiguities or risks that I speak of? 1) What is the likelihood of a price hike tomorrow? - It seems like it's 100% from your post but sprinkle some of that cynicism on it. 2.1) How prevalent is the secondary market of coins in New York - as in - If you were to buy 1,000 coins, how likely are you to sell them off and how long will it take you to liquidate your position, since for each dollar you spend today and not reclaim we would need to factor your cost of capital or opportunity cost of dollar allocated to the coins 2.2) If such market exists, are people going to trust you and buy them at the T+1 face value of $3 because they can get that price at the station anyway. Forgive me if I make a mistake here, I live in Toronto and it may be different from NYC but I highly doubt it. So chances are that you will need to bundle them 10-20 coins and sell them at a discount. 3) What is your demand for coins, as you will surely have a utility equal to at least $3 if you plan on continuing to buy and use these coins in the future. 4) How likely is it that the coins will continue to exist and not get an upgraded version. Consider for instance, the token that is now black will be discontinued and now the new coins in 1 week or 2 will become white and cost $3. So in affect most transportation operators give you a grace period and switch to a new mode of payment along with the price hike. That often happens in Toronto. In a year or so, can you return these coins for the price you bought them at? or the price of the new white coins.
You're all wrong. Metro Cards expire after 1 year. There's your brain teaser.
Edit: OP, I just want to point out how imperfect this example is as a brain teaser. A brain teaser is usually a problem with either very many or very few easily thought of answers, but with one that perfectly fits. This question is more akin to a run of the mill finance technical. My opinion..
Why would you use the market discount rate? What does this have to do with an equity? You aren't behind any debt holders, you are simply buying as close to a risk free investment as it gets assuming that the price remains at 3. The only discount I can see as reasonable is the risk free rate.
because you could either invest your 1000 dollars in tokens or invest in the market and get the market rate. That should be what you use to discount.
Ullam laboriosam qui soluta asperiores dicta et. Porro ex quaerat voluptate dolor. Repudiandae voluptate recusandae sunt consequatur ducimus in. Est et impedit debitis omnis consectetur iste quis ipsa. Ipsam voluptatem harum recusandae est sit laborum.
Sequi voluptatem et dolor minima sit aut. Ut commodi non doloremque sit minus veritatis. Eaque error dolor repellendus nobis.
See All Comments - 100% Free
WSO depends on everyone being able to pitch in when they know something. Unlock with your email and get bonus: 6 financial modeling lessons free ($199 value)
or Unlock with your social account...