Notes On Depreciating Assets
Hi there. In this personal finance post, I want to cover a little bit on depreciating assets and consumer items. This topic of depreciation is a bit theoretical but knowing this can help with purchasing decisions in personal finance settings. It can also be extended to business decisions but I do not have much expertise there so I just cover the personal finance cases.
Depreciation As A Decline In Value Over Time
The concept of depreciation is used in the accounting, business and finance areas but the regular person could use it too. Depreciation refers to a drop in value of an item over time. Investopedia refers to depreciation as how much of an asset's value is used up. As soon as a brand new item is purchased, that item loses value or depreciates. Generally, people prefer new items over used items. Used cars, used clothes, used video games, used equipment in a lot of cases carry less value than their new counterparts.
Some Mathematics Involved With Depreciation
Depreciating items generally do not lose all of its value right away after purchases. The value of many items goes down over time and aims to eventually reaches 0. Items such gas stoves, cars, computers, furniture, yachts and printers still has utility until it does not work or if gets replaced by something newer and better.
If it is something like underwear, the resale price of such an item would be zero. Who wants to buy used underwear??!!
Depreciating Car Example - Constant Depreciation Annual Rate
For this example, assume that a new $20000 USD car declines in value by $1000 USD after each year of usage. The value of this car decreases until the value of the car reaches 0.
I have included a partial table for the value of this car along with a graph.
|Year #||Value of Car ($USD)|
If you were to graph the above table, it would look something like the picture below. Replace the number of periods on the x-axis with the number of years.
What If The Value Of An Item Does Not Go Down At The Same Rate?
The previous example is nice and simple as the value of the car goes down by the same amount over time. What if the value of items goes down at different rates? A linear model does not work.
With cars and other depreciating assets, the depreciation percentage amount may not be the same between years. A graph would typically look like an exponential decay. This decay would most likely look like a smooth decrease into a flat line. (Image Source: Math Warehouse)
Cars in general do depreciate in value over time. Used car prices are lower than their new versions. Used cars may have wear and tear, damages and defects which would reduce the price. There are cases when cars that have been used appreciate in value and go up in price.
Some collectibles such as Pokemon cards, baseball cards, art pieces, video games such as classic Nintendo 64 Mario games, etc. do not depreciate in value. They could also depreciate in value at first but then gain in value all of a sudden.
For those who are price conscious, buying used books, used clothes, used equipment, used furniture and used cars can provide significant savings versus buying new. A used book may have not be in perfect condition but it can be readable. Some used clothes, equipment and used cars can be still in good condition. Do remember the phrase "Buyer Beware" when it comes to these type of purchases. These lower prices do carry risk.
The math models shown above are not always accurate. There is the saying that are "All models are wrong but some are useful." The depreciation math models shown here do have the right idea that the value of many items does decrease over time. For cases where the value of collectibles can go up, that is not so much math as it is more of economics, finance and human psychology.
EDIT: Fixed a few typos.
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