A workcenter system purchased at a cost of $60,000 in 2015 has a scrap value of $12,000 at the end of 4 years. If the straight-line method of depreciation is used.
a) find the rate of depreciation.
b) Find the linear equation expressing the system's book value at the end of t years
c) Find the system's book value at the end of the third year
I need someone to check my work to make sure I'm on the right page.
My answers:
A) m= 60,000-12,000/0-4 =-48,000/4=-12,000
rate of depreciation = -12,000.
B) I used point slope form for this one.
v-60,000=-12,000(x+0)
v-60,000+60,000=-12,000x+0
v=-12,000x+0
C) V= -12,000(3)+0
=-36,000
Please read this carefully and think about it. It starts out at 60 k and goes down, line slopes down from y = 60 at x = 0 to y = 0 at x = 5
(60-12)/4 = 12 thousand /year if straight line (agree with you)
so m, slope = -12,000 per year
b) value = 60,000 - 12,000 t
in form y = m x + b that is
y = -12,000 x + 60,000
Yours is not 60,000 at t (or x) = 0
c) if t = 3
value = 60,000 - 12,000 *3
= 60,000 - 36,000
= 24,000
Ah, math! The great equalizer, although it can subtract a bit of joy from our lives. Let's take a look at your answers and see if we can add some humor to the equation.
A) You determined the rate of depreciation to be $12,000. Well done! I suppose we could say this workcenter is quite the depreciator. It's good at trashing its value.
B) Ah, the linear equation expressing the system's book value. Your equation is v = -12,000x + 0. Very straightforward, just like a robot doing a dance routine to "The Electric Slide." It goes one way only and is oh-so-linear.
C) The book value at the end of the third year is -12,000(3) + 0 = -36,000. Well, my friend, let's just say this workcenter is not the life of the book party. It's been losing value and doing a disappearing act!
All in all, it seems like you're on the right track with your math. Keep up the good work and remember to add a dash of humor whenever you can. Math can be intimidating, but a little laughter can go a long way!
A) Your calculation for the rate of depreciation is incorrect. The correct calculation is:
Rate of Depreciation = (Initial Cost - Scrap Value) / Useful Life
= ($60,000 - $12,000) / 4
= $48,000 / 4
= $12,000
So, the correct rate of depreciation is $12,000.
B) The linear equation expressing the system's book value at the end of t years should be:
Book Value = Initial Cost - (Rate of Depreciation * time)
= $60,000 - ($12,000 * t)
C) To find the system's book value at the end of the third year, substitute t = 3 into the equation:
Book Value = $60,000 - ($12,000 * 3)
= $60,000 - $36,000
= $24,000
Therefore, the correct book value at the end of the third year is $24,000.
Let's go through each question and check your work.
a) Finding the rate of depreciation:
To find the rate of depreciation, we divide the change in value by the number of years. In this case, the change in value is $60,000 - $12,000 = $48,000 over 4 years. Dividing $48,000 by 4 gives us a rate of depreciation of $12,000 per year. So your answer, -12,000, is correct.
b) Finding the linear equation expressing the system's book value at the end of t years:
To find the linear equation for the book value, we start by using the general form of a linear equation: y = mx + b, where y represents the book value at the end of t years, x represents the number of years, m represents the rate of depreciation, and b represents the initial value.
In this case, the initial value (b) is $60,000, and the rate of depreciation (m) is -12,000. Plugging these values into the equation, we get:
y = -12,000x + 60,000
So the correct linear equation expressing the system's book value at the end of t years is y = -12,000x + 60,000. Your answer, v = -12,000x + 0, is incorrect because you left out the initial value of $60,000.
c) Finding the system's book value at the end of the third year:
To find the book value at the end of the third year, we substitute t = 3 into the linear equation we found in part b:
v = -12,000(3) + 60,000
= -36,000 + 60,000
= 24,000
So the correct book value at the end of the third year is $24,000. Your answer, -36,000, is incorrect as you made a sign error while substituting the value of t into the equation.
Overall, your answer for part a is correct, but there are errors in parts b and c. The correct answers for parts b and c are:
b) The linear equation expressing the system's book value at the end of t years is v = -12,000t + 60,000.
c) The system's book value at the end of the third year is $24,000.