Thought Experiment for work: useful lives of populations

BRDaniel

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I work as an auditor and although this is probably something I wouldn't implement I have been trying to figure it out and would appreciate any help.

When analyzing Fixed Assets I was trying to determine, more or less, where the population was in terms of their useful lives. I wanted to do this to help set an expectation of what Repairs and Maint. expenses should do since the thinking is that as assets age they will require more repairs and vice versa. My first though was to simply calculate each item's remaining life as a percentage and then simply average those percentages but that doesn't seem right. Shouldn't I have some kind of weighting as the repairs for various assets would vary based on the cost of said asset (you wouldn't spend $1000 to fix a $500 computer but $1000 on a $100,000 building you would). I also tried to plot a distribution of the percentages and see if it the distribution was skewed left or right to get an indication of where the bulk of the data lay by comparing where the mean and median were in relation to each other but that still doesn't seem to fix the idea of weighting.

I am looking more for help on the theory and approach than the actual math, at least at this time, as I would very much like to try to figure this out on my own, I just need some help. I have always been fascinated by math but just not smart enough by half to get a degree in it so I am just hoping to learn some things. Below I have posted some sample data for reference.

Thanks for reading.


Asset Type
Useful LifeYrs in ServiceOriginal CostAmt DepreciatedRemaining BasePct of Life used
Building203100,00015,00085,00015%
Building2531180,000151,20028,80084%
Computer541,00080020080%
Computer511,00020080020%
Truck7620,00017,1432,85786%
Truck7218,0005,14312,85729%
Car7225,0007,14317,85729%
Assembly Eq15865,00034,66730,33353%
 
You should not average percents, or even weight them. This may produce a reasonable approximation, but it is unlikely to be particularly useful in ever case.

Ho di you calculate the individual percentages? However you did that, try in in total and see what happens.
 
I calculated the percents by dividing "yrs in service" by "useful lives"**.

So by totaling the two columns I get 51-52%. This will give me an accurate state of the age of the population? It seems very simple. I did try this as well before I posted my question but it just never seemed that it would be correct...

Thank you for your answer!


** The second row should read 21 yrs in service. I fat fingered the number.
 
First, I would think about this terms of a small number of CLASSES of assets, e.g., buildings, vehicles, computer, and so on. The reason is that the pattern of annual maintenance expenses over the expected life of the asset may be very different among different asset classes.

Second, I'd use something like multiple regression to find how annual maintenance expense varies in response to the net book value of a given asset class and the weighted average age of that class, where the weights would be net book values of the assets in that class.

My thinking is this. Within each asset class, if there is a reasonably stable historical pattern relationship among annual maintenance expense, net book value, and the average age of the assets, you can then calculate a probable range for that expense in the most current year. When the expense is outside that expected range, you have a signal that it should be given extra scrutiny.
 
@JeffM

This makes perfect sense. I think a few engagements back I wanted to do something similar for a client but my senior discouraged it so I figured it must have been wrong.

Thank you very much!
 
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