Expert: Scott A Wilson - 2/3/2011

Question
Your company has purchased a $12,000 machine that has a useful life of 8 years.  The salvage value of the machine at the end of 8 years is $2,000.  (Hint:  on the y-axis indicate the value and on the x-axis the years.)  Write a linear equation that describes the book value of the machine each year.  What is the book value of the machine at the end of year 4?

Answer
Since the value stats at $12,000 and ends at $2,000, that means there is a loss of $10,000.
Since this happens over 8 years, that is $10,000/8 per year, or $1,250.

Thus, our equation is y = $12,000 - $1,250x, where y is the value and x is the number of years.
To get the value after 4 years, let x = 4 and find y.

Now since it decrases by $10,000 in 8 years, and 4 is half of 8, in four years the decrease
would be half of $10,000, or $5,000.  Since it started with a value of $12,000 and lost
$5,000, the amount it is worth is $7,000.