An office building worth $1 million when completed in 2010 is being depreciated linearly over 25 years. What was the book value of the building in 2012? What will it be in 2024? (Assume the scrap value is $0.)
so, the building loses 1000000/25 = $40,000 per year.
so, its value (in thousands) after x years is
1000 - 40x
Well, I must say, this building seems to have quite the destiny ahead of it! Now, let me get my humor calculator out and crunch some numbers for you.
Since the building is being depreciated linearly over 25 years, we can divide the cost evenly across those years. So, each year, the building's value decreases by 1/25th of its original value.
In 2012, let's calculate: 2012 - 2010 = 2 years have passed. Applying our depreciation rate, the building's value would have decreased by 2/25th of its original value.
So, the book value in 2012 would be $1 million - (2/25) * $1 million = $1 million - $80,000 = $920,000. Ta-da!
Now, let's fast forward to 2024: 2024 - 2010 = 14 years have passed. Using the same depreciation rate, the building's value would have decreased by 14/25th of its original value.
So, the book value in 2024 would be $1 million - (14/25) * $1 million = $1 million - $560,000 = $440,000.
Well, it looks like this building is ready for some new tenants!
To find the book value of the building in 2012, we need to determine the annual depreciation amount.
The building is being depreciated linearly over 25 years, so we can calculate the depreciation per year by dividing the initial value of $1 million by the lifespan of 25 years:
Depreciation per year = Initial value / Lifespan
= $1,000,000 / 25
= $40,000 per year
To find the book value in 2012, we need to determine the number of years that have passed since 2010:
Years passed = 2012 - 2010
= 2 years
Book value in 2012 = Initial value - (Depreciation per year × Years passed)
= $1,000,000 - ($40,000 × 2)
= $1,000,000 - $80,000
= $920,000
Therefore, the book value of the building in 2012 would be $920,000.
To find the book value in 2024, we need to determine the number of years that have passed since 2010:
Years passed = 2024 - 2010
= 14 years
Book value in 2024 = Initial value - (Depreciation per year × Years passed)
= $1,000,000 - ($40,000 × 14)
= $1,000,000 - $560,000
= $440,000
Therefore, the book value of the building in 2024 would be $440,000.
To find the book value of the building in a given year, we need to use the formula for linear depreciation.
Linear depreciation calculates the decrease in value of an asset over time, assuming a constant rate of depreciation each year. The formula for linear depreciation is:
Depreciation per year = (Initial value - Scrap value) / Useful life
Given the information in the question:
Initial value (cost when completed) = $1 million
Scrap value = $0
Useful life = 25 years
Using the formula, we can calculate the depreciation per year:
Depreciation per year = ($1,000,000 - $0) / 25 = $40,000
Now, let's calculate the book value in 2012:
To find the book value in 2012, we need to calculate the number of years that have passed since 2010, which is 2 years.
Book value in 2012 = Initial value - (Depreciation per year x Number of years)
Book value in 2012 = $1,000,000 - ($40,000 x 2) = $920,000
Therefore, the book value of the building in 2012 is $920,000.
Similarly, let's calculate the book value in 2024:
To find the book value in 2024, we need to calculate the number of years that have passed since 2010, which is 14 years.
Book value in 2024 = Initial value - (Depreciation per year x Number of years)
Book value in 2024 = $1,000,000 - ($40,000 x 14) = $440,000
Therefore, the book value of the building in 2024 will be $440,000.