Expert: Sherry Wallin - 6/22/2011

Question
The price of a ;arge piece of construction equipment purhcased by Hass Construction Company was $53,500. It cost $1,275 for delivery and $2,750 for installation. The salvage value at the end of a 4 year life is $7,500. Using the straight-line depreciation method, calculate the annual depreciation for year 3.

Answer
Darrell~

The first thing you need to calculate is the total cost which will be the price of the equipment plus the delivery and installation. This is your initial investment or it's value to you. So let y be the value thus y = 53500 + 1275 + 2750 = 57525
So at year 0 your value is 57525. They tell you that at year 4 the value is 7500. These two bits of information can be translated into two ordered pairs on a graph of (time, value) => (0, 57525) and ( 4, 7500). This is enough information to calculate the slope of the line that describes the salvage value. The words "straight-line" depreciation tell us that the equation will be a line.

m = (57525-7500)/(0-4) = 50025/-4 = -12506.25
Using the point slope form of the equation of a line y-y1 = m(x-x1) : y - 57525 = -12506.25(x-0) =>
y - 57525 = -12506.25x =>
y = -12506.25x + 57525

Now all you need to do is calculate when x = 3...
y = -12506.25(3) + 57525 =>
y = 20006.25 =>
this tells us the value at year 3 is $20006.25

Math Prof