Expert: Steve Holleran - 3/10/2007

Question
I hate word problems and I need help.
The problem readsA company is considering two ways to depreciate a truck: straight line or by a fixed percentage. If each way begims with a value of 25,000 and ends 5 years later with a value of 1,000, which way will result in the bigger change in value during the first year? During the last year?
I dont get it
Alicia


Answer
Hi Alicia,

To tell you the truth, I don't know of too many people who LIKE word problems!!  Anyway, I think we can take care of this without tearing hairs out.

Okay, the first part is the easiest.  For straight-line depreciation, you simply divide the decrease in value by the time it takes to occur:  $25000 - $1000 = $24,000 decrease over 5 years is $24,000 / 5 = $4800 per year.
So, during the first year, the truck depreciates $4800.

For a fixed percentage, lets call the percent of depreciation r.  Then the formula we need is :

    Value = Original Value * (1 - r)^t

[The quantity in parentheses is 1-r because its a depreciation.  For example, if the depreciation were 4% per year, the multiplier would be 1 - .04 = .96]

So, we now have:

         1,000 = 25,000 * (1 - r)^5

Dividing by 25,000:

          1/25 = (1 - r)^5

          .04  = (1 - r)^5

Taking the fifth root of .04:

          .5253 = 1-r   .  This is actually the multiplier we need, but the rate of depreciation, r, is
1 - .5253 or 0.4747 = 47.47%

So after the first year, the truck's value is calculated by

        V = 25,000 (.5253)^1 = $13, 132  

which means the truck lost 25,000 - 13,132 = $11,868 in value.

You can do this very easily if you have a graphing calculator by entering 25,000 * .5253 and getting 13,132,
then just entering ANS * .523 successively, and you'll get the values after each year.  You should get the following answers:

13,132  

6890

3617

1899

997    (These are all approximations, and rounded).

So, during the last year, fixed % method had the truck losing only 1899-997 = 902 in value, and straight-line was still 4800.

I hope this is what you were looking for, and helps you out.

Steve Holleran