When should you stop renting?

tags , , , dot 3 comments
2010/03/12
335 words
by Fredrik Olsen

I have a problem I’ve been thinking about on and off for a while. When should you stop renting something and buy it instead?

The situation in which I am confronted with this is currently when I play badminton. At the place where I play it costs 20 SEK to rent a racket. But you can buy a fair-quality racket for around 200 SEK.

When you start playing you should obviously rent because you don’t know if you’re going to keep playing, but after how many times should you stop renting and just buy a racket?

If you play 10 times you’ve spent just as much money on renting as if you would have bought a racket on day 1. The cost of the racket is then 200% of the buying price.

I don’t think you should wait 10 rounds of play before you buy, because you can be fairly sure you are going to play more than 10 times before you’ve played 10 times. But I’m not sure where to draw the limit. I think after about 5 times I’m pretty sure I’m going to play 10 times too. So then cost of the racket is 150% of the buying price.

On the other hand, if you buy the racket right away and not play 10 times, you’ve only spent 100% of the buying price but the money might be wasted. If you only play twice and bought the racket right away, you’ve wasted 80% of the cost. What’s better: Wasting some of the cost or adding to the cost?

Obviously where you draw the line varies on situation and the amount of money involved, but my question is: How do you calculate where to draw the line?

I think that when the cost is somewhere between 150-200% of the buying price it’s the right time to buy. But how do I calculate exactly where the right place is? Leave your thoughts in the comments!

Update: I just found out a fair-quality racket cost more than 200, but my question remains valid.

3 comments

tetris

  • http://eferm.com Emanuel

    It’s more complex than that, obviously :) 200 kr today are worth more than 200 kr tomorrow, just as there should be a factor that increases your willingness to play if you buy the racket beforehand.

    Let’s say the probability of you playing your second time is 0.9 in a normal case, then diminishing linearly, -1% for each session. If you buy the racket, lets say that increases your chance of playing more times with 10%:

    Probability of playing 10 times (before buying racket): 0.9*0.8*…*0.1 = 25%
    Probability of you playing 10 times, if you buy the racket on day one: 55%! More than double the probability.

    Then, let’s say the consumer price index increases with 1kr/year. That’s 50/365 kr savings if you buy the racket on day one, as compared to waiting 50 days (if you play every 5 days).

    Money spent if you buy the racket on the tenth session: 20×10 + (200 + 50/365) = 400.14 kr
    Money spent if you buy the racket on day one: 20×10 = 200 kr

    So… by buying the racket on day one you more than double your likelihood of playing 10 times, AND you spend less than half of the money! Incredible.

    /Emanuel, the squash racket salesman.

  • http://eferm.com Emanuel

    Footnote: obviously the probability distribution of playing squash does NOT follow an ever decreasing trend; after X times played it becomes a habit and thus entering a phase where different estimations need to be made.

    Just to add to the rigor of my argument ;)

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