Chapter 11, Problem 13P

To determine

(a)

The depreciation schedule using straight line depreciation.

Answer to Problem 13P

The depreciation schedule using straight line depreciation is shown below.

Year $\left(t\right)$	Depreciation $d_{\text{t}}=\frac{B-S}{n}$
$1$	$\$3,600$
$2$	$\$3,600$
$3$	$\$3,600$
$4$	$\$3,600$
$5$	$\$3,600$

Explanation of Solution

Given:

Cost of the handling device is $\$20,000$.

Time period is $5\text{years}$.

Salvage value is $\$2,000$.

Concept used:

Write the expression to calculate the depreciation value for the handling device

$d_{\text{t}}=\frac{B-S}{n}$ ...... (I)

Here, the depreciation value is $d_{\text{t}}$, the cost of the handling device is $B$, salvage value is $S$ and number of years is $n$.

Calculation:

Calculate the depreciation for the handling device.

Substitute $\$20,000$ for $B$, $\$2,000$ for $S$ and $5$ for $n$ in Equation (I).

$\begin{array}{c}{d}_{\text{t}}=\frac{\$20,000-\$2,000}{5}\\ =\$3,600\end{array}$

Calculate the depreciation for 5 years and enter them in a table below.

Year $\left(t\right)$	Depreciation $d_{\text{t}}=\frac{B-S}{n}$
$1$	$\$3,600$
$2$	$\$3,600$
$3$	$\$3,600$
$4$	$\$3,600$
$5$	$\$3,600$

Conclusion:

The depreciation schedule using straight line depreciation is shown below.

Year $\left(t\right)$	Depreciation $d_{\text{t}}=\frac{B-S}{n}$
$1$	$\$3,600$
$2$	$\$3,600$
$3$	$\$3,600$
$4$	$\$3,600$
$5$	$\$3,600$

To determine

(b)

The depreciation schedule using SOYD.

Answer to Problem 13P

The depreciation schedule using SOYD is shown below.

Year $\left(t\right)$	Depreciation $\left(d_{\text{t}}\right)$
$1$	$\$6,000$
$2$	$\$4,800$
$3$	$\$3,600$
$4$	$\$2,400$
$5$	$\$1,200$

Explanation of Solution

Concept used:

SOYD is known as sum of year’s digits depreciation.

Write the expression to calculate the depreciation of the handling device.

$\begin{array}{c}{d}_{\text{t}}=\frac{n-t+1}{SOYD}\left(B-S\right)\\ d_{\text{t}}=\frac{n-t+1}{\left[\frac{n\left(n+1\right)}{2}\right]}\left(B-S\right)\end{array}$ ...... (II)

Here, the depreciation value is $d_{\text{t}}$, total number of years is $n$, cost of the handling device is $B$, particular year is $t$ and salvage value after depreciable life is $S$.

Calculation:

Calculate the depreciation using SOYD for the handling device.

Substitute, $5$ for $n$, $\$20,000$ for $B$ and $\$2,000$ for $S$ in Equation (II)

$\begin{array}{c}{d}_{\text{t}}=\frac{5-t+1}{\left[\frac{5\left(5+1\right)}{2}\right]}\left(\$20,000-\$2,000\right)\\ =\frac{\left(6-t\right)}{15}\times \left(\$18,000\right)\\ =\$1,200\left(6-t\right)\end{array}$ ...... (III)

Calculate the depreciation value for 5 year.

Year $\left(t\right)$	Depreciation $\left(d_{\text{t}}\right)$
$1$	$\$6,000$
$2$	$\$4,800$
$3$	$\$3,600$
$4$	$\$2,400$
$5$	$\$1,200$

Here, calculate the depreciation from Equation (III).

Conclusion:

The depreciation schedule using SOYD is shown below.

Year $\left(t\right)$	Depreciation $\left(d_{\text{t}}\right)$
$1$	$\$6,000$
$2$	$\$4,800$
$3$	$\$3,600$
$4$	$\$2,400$
$5$	$\$1,200$

To determine

(c)

The depreciation schedule using double declining balance depreciation.

Answer to Problem 13P

The depreciation schedule using double declining balance depreciation is shown below.

Year $\left(t\right)$	Depreciation $\left(d_{\text{t}}\right)$
$1$	$\$8,000$
$2$	$\$4,800$
$3$	$\$2,880$
$4$	$\$1,728$
$5$	$\$1036.8$

Explanation of Solution

Concept used:

Write the expression to calculate the depreciation using double declining balance depreciation

$d_{\text{t}}=\frac{2}{n}\left(B-\text{Depreciation}\text{charge}\text{up}\text{to}\text{year}t\right)$ ...... (IV)

Here, the depreciation is $d_{\text{t}}$, number of years is $n$, cost is $B$.

Calculation:

Calculate the depreciation of the handling device for the first year.

Substitute $5$ for $n$, $\$20,000$ for $B$ and $0$ for depreciation charge up to year $t$ in Equation (IV).

$\begin{array}{c}{d}_{\text{t}}=\frac{2}{5}\left(\$20,000-\$0\right)\\ =\frac{2}{5}\times \$20,000\\ =\$8,000\end{array}$

Calculate the depreciation of the handling device for 5 years and enter it in a table below.

Year $\left(t\right)$	Depreciation charge up to year $t$	Depreciation $\left(d_{\text{t}}\right)$
$1$	$0$	$\$8,000$
$2$	$\$8,000$	$\$4,800$
$3$	$\$12,800$	$\$2,880$
$4$	$\$15,680$	$\$1,728$
$5$	$\$17,408$	$\$1036.8$

Conclusion:

The depreciation schedule using double declining balance depreciation is shown below.

Year $\left(t\right)$	Depreciation $\left(d_{\text{t}}\right)$
$1$	$\$8,000$
$2$	$\$4,800$
$3$	$\$2,880$
$4$	$\$1,728$
$5$	$\$1036.8$

To determine

(d)

The depreciation schedule using MACRS depreciation.

Answer to Problem 13P

The depreciation schedule using MACRS is shown below.

Year $\left(t\right)$	MACRS $\left(r_{\text{t}}\right)$	Cost $\left(B\right)$	Depreciation $d_{\text{t}}=r_{\text{t}}\times B$
$1$	$33.33\%$	$\$20,000$	$\$6,666$
$2$	$44.45\%$	$\$20,000$	$\$8,890$
$3$	$14.81\%$	$\$20,000$	$\$2,962$
$4$	$7.41\%$	$\$20,000$	$\$1,482$

Explanation of Solution

Concept used:

Write the expression to calculate the depreciation value for the motorboat.

$d_{\text{t}}=B\times r_{\text{t}}$ ...... (V)

Here, the depreciation value is $d_{\text{t}}$, the cost of the plane is $B$ and the MACRS percentage is $r_{\text{t}}$.

Calculation:

Using MACRS GDS 4 year property table calculate the depreciation for the handling device.

Calculate the depreciation for handling device.

Substitute $\$20,000$ for $B$ and $33.33\%$ for $r_{\text{t}}$ in Equation (V).

$\begin{array}{c}{d}_{\text{t}}=\$20,000\times 33.33\%\\ =\$6,666\end{array}$

Calculate the depreciation for 5 years and enter them in a table below.

Year $\left(t\right)$	MACRS $\left(r_{\text{t}}\right)$	Cost $\left(B\right)$	Depreciation $d_{\text{t}}=r_{\text{t}}\times B$
$1$	$33.33\%$	$\$20,000$	$\$6,666$
$2$	$44.45\%$	$\$20,000$	$\$8,890$
$3$	$14.81\%$	$\$20,000$	$\$2,962$
$4$	$7.41\%$	$\$20,000$	$\$1,482$

Conclusion:

The depreciation schedule using MACRS is shown below

Year $\left(t\right)$	MACRS $\left(r_{\text{t}}\right)$	Cost $\left(B\right)$	Depreciation $d_{\text{t}}=r_{\text{t}}\times B$
$1$	$33.33\%$	$\$20,000$	$\$6,666$
$2$	$44.45\%$	$\$20,000$	$\$8,890$
$3$	$14.81\%$	$\$20,000$	$\$2,962$
$4$	$7.41\%$	$\$20,000$	$\$1,482$