Question 1181198: A piece of machine is purchased for $1,000,000. Accountants of the firm decided to use straight line
method with the machine being depreciated in 12 years and have an estimated salvage value of
$123,000. Letting V is equal to the book value of the machine and t is the age of machine,
a) Determine the function V = f(t)
b) Determine the book value of machine after 8 years & 11.5 years by using the function
determined in part a
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to determine the function for the book value and calculate the book value after 8 and 11.5 years:
**a) Determine the function V = f(t):**
1. **Calculate the annual depreciation:**
* Depreciable amount = Purchase price - Salvage value
* Depreciable amount = $1,000,000 - $123,000 = $877,000
* Annual depreciation = Depreciable amount / Useful life
* Annual depreciation = $877,000 / 12 years = $73,083.33 per year (approximately)
2. **Write the function:**
Since we're using straight-line depreciation, the book value decreases linearly over time. The function will be in the form:
V(t) = Initial book value - (Annual depreciation * t)
V(t) = $1,000,000 - $73,083.33t
**b) Determine the book value after 8 years and 11.5 years:**
Using the function V(t) = $1,000,000 - $73,083.33t:
* **After 8 years:**
V(8) = $1,000,000 - ($73,083.33 * 8)
V(8) = $1,000,000 - $584,666.64
V(8) = $415,333.36
* **After 11.5 years:**
V(11.5) = $1,000,000 - ($73,083.33 * 11.5)
V(11.5) = $1,000,000 - $840,458.295
V(11.5) = $159,541.705
**Answers:**
* a) The function V = f(t) is: V(t) = $1,000,000 - $73,083.33t
* b) The book value after 8 years is approximately $415,333.36.
* b) The book value after 11.5 years is approximately $159,541.71.
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