A piece of machinery is purchased for $400,000. Accountants have decided to
use a straight-line depreciation method
That means we have the equation of a line of the form y=mx+b, except we
change the letters to V = mt+b, and that when t=0, V=400000. In other words,
the line begins at the point (t,V) = (0,400000), and we can substitute 0 for
t and 400000 for V and get:
V = mt+b
400000 = m∙(0)+b
400000 = 0+b
400000 = b
We now know what b is. So the formula is now
V = mt+400000
with machine being fully depreciated after 10 years.
That means that when t=10 years, the value V is 0 (it is worthless).
So the line ends at the point where t=10 and V=0, which is the point (10,0).
We substitute that point in the equation
V = mt+400000
0 = m∙(10)+400000
-400000 = 10m
-40000 = m
So now we know m. so we substitute -40000 for m and we have:
V = mt+4000000
V = -40000t+4000000
Letting V equal the book value of the machine [at time t anywhere between
t=0 and t=10.]
Which we did.
a) Assuming that there is no salvage value, determine the function V=f (t).
We just did. "No salvage value" and "fully depreciated" mean the same thing. So
V = -40000t+400000 [answer to (a) part)]
b) If the machine can be resold after 10 years for $25,000. Determine the
function V=f (t).
We go back to what we had just before we were told that is was worthless
when t=10 years. It is no longer assumed worthless when t=10 years, for now
it is worth 25000 when t=10 years. The formula before we assumed it was
worthless when t=10, was this.
V = mt+400000
Now when t=10, V=25000, [not 0], so the line now ends at the point
(10,25000).
So we substitute t=10 and V = 25000
25000 = m∙(10)+400000
25000 = 10m+400000
-375000 = 10m
-37500 = m
Now we know m, so we substitute -37500 for m and we have:
V = mt+4000000
V = -37500t+4000000 [answer to (b) part]
Edwin
