Chapter 11, Problem 51P

To determine

i.

Book Value after 2 years.

Answer to Problem 51P

Book Value after 2 years is $40800.

Explanation of Solution

Given:

Useful Life = 5 years

Cost of asset = $85000

Salvage Value = $15000

ADR life = 8 years.

Calculation:

MACRS depreciation is calculated by using the following formula=

$d_t=B\times r_t$

$d_t$ is the depreciation charge in any year t. B is the cost of the asset made ready for use.

$r_t$ is the appropriate MACRS schedule for the asset by MACRS depreciation.

Recovery Year, t (year)	MACRS
1	20%
2	32%
3	19.20%
4	11.52%
5	11.52%
6	5.76%
	100%

The asset is a 5-year property with asset depreciation range (ADR) class life of more than 10 years and less than 16 years.

Book Value is calculated of an asset at the end of 1^st year of its useful life period.

$\begin{array}{l}B{V}_3=\$85000-\left(3\times \$8750\right)\\ =\$85000-\$26250\\ =\$58750\end{array}$

$B{V}_t$ is the Book Value of the asset at any year t, B is the purchase cost of the asset and ${\displaystyle {\sum }_{t=1}^t{d}_t}$ is sum of depreciation charges till any year t.

T = 1

B = $85000

$d_t=\$17000$

$\begin{array}{l}B{V}_t=B-{\displaystyle {\sum }_{t=1}^t{d}_t}\\ =B-d_t\\ =\$85000-\$17000\\ =\$68000\end{array}$

Years	Depreciation charge	Book Value
1	17000	68000
2	27200	40800
3	16320	24480
4	9792	14688
5	9792	4896
6	4896	0
7	0	0
8	0	0
	85000

Conclusion:

Book Value after 2 years is $40800.

To determine

ii.

Book Value after 4 years.

Answer to Problem 51P

The book value of the asset after 4 years of its useful life is $14688.

Explanation of Solution

Given:

Useful Life = 5 years

Cost of asset = $85000

Salvage Value = $15000

ADR life = 8 years.

Calculation:

The book value of the asset after 4 years of its useful life is $14688.

Years	Depreciation charge	Book Value
1	17000	68000
2	27200	40800
3	16320	24480
4	9792	14688
5	9792	4896
6	4896	0
7	0	0
8	0	0
	85000

Conclusion:

The book value of the asset after 4 years of its useful life is $14688.

To determine

iii.

The accumulated depreciation charge of the asset through the 5^th year.

Answer to Problem 51P

The accumulated depreciation charge of the asset through the 5^th year is $80104.

Explanation of Solution

Given:

Useful Life = 5 years

Cost of asset = $85000

Salvage Value = $15000

ADR life = 8 years.

Calculation:

The accumulated depreciation charge of the asset through the 5^th year

${\displaystyle {\sum }_{t=1}^t{d}_t=d_1+d_2+d_3+\mathrm{.........}+d_t}$

Here, ${\displaystyle {\sum }_{t=1}^t{d}_t}$ is the accumulated depreciation charge of the asset till year t and d₁, d₂.... Are depreciation charges for different years.

Year	depreciation (d)
1	$17,000
2	$27,200
3	$16,320
4	$9,792
5	$9,792
	$80,104

Conclusion:

The accumulated depreciation charge of the asset through the 5^th year is $80104.

To determine

iv.

Depreciation charge of the asset for the 6^th year.

Answer to Problem 51P

The depreciation charge of the asset for the 6^th year is $4896.

Explanation of Solution

Given:

Useful Life = 5 years

Cost of asset = $85000

Salvage Value = $15000

ADR life = 8 years.

Calculation:

Years	Depreciation charge	Book Value
1	17000	68000
2	27200	40800
3	16320	24480
4	9792	14688
5	9792	4896
6	4896	0
7	0	0
8	0	0
	85000

Conclusion:

The depreciation charge of the asset for the 6^th year is $4896.

To determine

v.

The book value of the asset for the 8^th year.

Answer to Problem 51P

The book value of the asset for the 8^th year, using MACRS is $0.

Explanation of Solution

Given:

Useful Life = 5 years

Cost of asset = $85000

Salvage Value = $15000

ADR life = 8 years.

Calculation:

Book Value is calculated of an asset at the end of 1^st year of its useful life period.

Useful Life = 5 years

Cost of asset = $85000

Salvage Value = $15000

ADR life = 8 years.

$\begin{array}{l}B{V}_3=\$85000-\left(3\times \$8750\right)\\ =\$85000-\$26250\\ =\$58750\end{array}$

$B{V}_t$ is the Book Value of the asset at any year t, B is the purchase cost of the asset and ${\displaystyle {\sum }_{t=1}^t{d}_t}$ is sum of depreciation charges till any year t.

T = 1

B = $85000

$d_t=\$17000$

$\begin{array}{l}B{V}_t=B-{\displaystyle {\sum }_{t=1}^t{d}_t}\\ =B-d_t\\ =\$85000-\$17000\\ =\$68000\end{array}$

Years	Depreciation charge	Book Value
1	17000	68000
2	27200	40800
3	16320	24480
4	9792	14688
5	9792	4896
6	4896	0
7	0	0
8	0	0
	85000

Conclusion:

The book value of the asset for the 8^th year, using MACRS is $0.

To determine

vi.

Book Value at the end of 3^rd year using straight Line Method.

Answer to Problem 51P

The book value of the asset after 3^rd year is $58570.

Explanation of Solution

Given:

Useful Life = 5 years

Cost of asset = $85000

Salvage Value = $15000

ADR life = 8 years.

Calculation:

Straight Line depreciation Method:

$d_t=\frac{B-S}{N}$

$d_t$ is the depreciation charge in any year t, N is the number of years in a depreciable life, B is the cost of the asset made ready for use.

T = 1 year

B = $85000

S = $15000

N = 8

$\begin{array}{l}{d}_t=\frac{B-S}{N}\\ d_t=\frac{\$85000-\$15000}{8}\\ =\$8750\end{array}$

Straight Line depreciation is constant throughout the depreciable Life. Thus, the depreciation charge for the asset is $8750 for every year throughout the depreciable life of the asset.

Book Value at the end of 3^rd year

$\begin{array}{l}B{V}_t=B-{\displaystyle {\sum }_{t=1}^t{d}_t}\\ =B-n{d}_t\end{array}$

$\begin{array}{l}B{V}_3=\$85000-\left(3\times \$8750\right)\\ =\$85000-\$26250\\ =\$58750\end{array}$.

Conclusion:

Thus, the book value of the asset after 3^rd year is $58570.

To determine

vi.

Book value of the asset after 8^th year.

Answer to Problem 51P

Book value of the asset after 8^th year is $15000.

Explanation of Solution

Given:

Useful Life = 5 years

Cost of asset = $85000

Salvage Value = $15000

ADR life = 8 years.

Calculation:

$\begin{array}{l}B{V}_t=B-{\displaystyle {\sum }_{t=1}^t{d}_t}\\ =B-n{d}_t\end{array}$

$\begin{array}{l}B{V}_8=\$85000-\left(8\times \$8750\right)\\ =\$85000-\$70000\\ =\$15000\end{array}$.

Conclusion:

Thus, the book value of the asset after 8^th year is $15000.