Nelson from Financial Uproar was good enough to send me an e-mail asking if I was still alive last week. My wife and I have been pretty focused on a new duplex we bought (details to come in future posts), which is why I haven’t posted in quite some time. Thanks again Nelson, it’s nice to be missed!
A Reddit user recently asked an interesting question about an analytical method for calculating opportunity cost in a car transaction he made (pdf in case original is lost). I felt like the commenters kind of blew it with their suggestions, often only offered “rules of thumb” or general principles in a situation that was quite tractable.
What is Opportunity Cost?
Opportunity cost is a concept from economics that looks at what you miss out on doing one thing instead of another. If someone only had enough money to buy a ticket to a baseball game or a video game, in each case the opportunity cost is the other item – if he buys the ticket, his opportunity cost is the hours of entertainment he’d have gotten playing the video game; if he buys the video game, his opportunity cost is missing the enjoyment of watching baseball live in person.
So What’s The Opportunity Cost Here?
He’s contrasting two situations, the first where he bought a used car for $630, invested 3 hours of work into the transactions and sold it for $800. The other alternative was where he would have bought it for $630, paid $1,000 for repairs with between a week and 1.5 weeks of work on the repairs, then sold it for $2,800.
We’ll ignore the time value of money (buying and selling the first day vs. keeping the car for a week and a half) and any uncertainty in the alternative situation – the repair might have been easier (less than 40 hours) or harder (more than 60 hours) than he anticipated. He also might not have sold it for $2,800.
In both situations his purchase price is the same, so the only real difference between the two is how much of his time he puts into it and how much money he makes from it. These can be easily compared.
In the first case, he made $170 in 3 hours, so his labor was worth $56.67 per hour (170 /3).
In the second case, he would have made $1,170 (2800 – 1000 – 630). If we assume the repairs went well and he finished them in a 40 hour work week, his time would have been worth $29.25 per hour (1170 / 40). If it took him the week and a half, his time would have been worth $19.50 per hour.
Dividing the estimated net value of the repaired car, $1,170, by the hourly value of his time, $56.67 / hour, we come up with 20.65 hours. If he could do the repairs in less time than this, it’s worth doing them. If it takes him longer, it’s better to sell the car unrepaired.
Therefore, he made the right decision buying and selling the car unrepaired for $800 with 3 hours work. His time would be better spent using the 40 – 60 hours that he would have spent repairing the car on trying to buy other cars cheap then resell them.
If we value his time at $56.67 per hour, the opportunity cost of repairing the car would have been a loss of $1096.80 (56.67 * 40 – 1170) in the 40 hour repair case and $2304.40 (56.67 * 60 – 1170) in the the 60 hour repair case.
Are There Any Other Considerations?
It could be the case that buying this car for $630 and reselling it for $800 in three hours was a rare, magical, unrepeatable event that he is unlikely to achieve in the future. In this case, he would want to decide if the hourly rate for the repairs ($19.50 – $29.25) is more or less than his time is usually worth. If he works for minimum wage, it might be worth the opportunity to make more money than he usually makes working on the car. If he usually makes more than $30 / hour, than he’s certainly better off making the quick sale and selling it for $800 unrepaired.