Chapter 11, Problem 16P

To determine

(a)

The depreciation schedule using MACRS depreciation.

Answer to Problem 16P

The depreciation schedule using MACRS is shown below.

Year $\left(t\right)$	MACRS $\left(r_{\text{t}}\right)$	Cost $\left(B\right)$	Depreciation $d_{\text{t}}=r_{\text{t}}\times B$
$1$	$14.29\%$	$\$20,000$	$\$7,145$
$2$	$24.49\%$	$\$20,000$	$\$12,245$
$3$	$17.49\%$	$\$20,000$	$\$8,745$
$4$	$12.49\%$	$\$20,000$	$\$6,245$
$5$	$8.93\%$	$\$20,000$	$\$4,465$
$6$	$8.92\%$	$\$20,000$	$\$4,460$
$7$	$8.93\%$	$\$20,000$	$\$4,465$
$8$	$4.46\%$	$\$20,000$	$\$2,230$

Explanation of Solution

Given:

Cost of the crystal extraction device is $\$50,000$.

Time period is 8 years.

Salvage value is $\$10,000$.

Concept used:

Write the expression to calculate the depreciation value for the crystal extraction device.

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

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

Calculation:

Crystal extraction device comes under MACRS GDS “all other property not assigned to another class” designation.

Using MACRS GDS 8 year property table calculate the depreciation for the crystal extraction device.

Calculate the depreciation for crystal extraction device.

Substitute $\$50,000$ for $B$ and $14.29\%$ for $r_{\text{t}}$ in Equation (I).

$\begin{array}{c}{d}_{\text{t}}=\$50,000\times 14.29\%\\ =\$7,145\end{array}$

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 $d_{\text{t}}=r_{\text{t}}\times B$
$1$	$14.29\%$	$\$20,000$	$\$7,145$
$2$	$24.49\%$	$\$20,000$	$\$12,245$
$3$	$17.49\%$	$\$20,000$	$\$8,745$
$4$	$12.49\%$	$\$20,000$	$\$6,245$
$5$	$8.93\%$	$\$20,000$	$\$4,465$
$6$	$8.92\%$	$\$20,000$	$\$4,460$
$7$	$8.93\%$	$\$20,000$	$\$4,465$
$8$	$4.46\%$	$\$20,000$	$\$2,230$

Conclusion:

The depreciation schedule using MACRS is shown below

Year $\left(t\right)$	MACRS $\left(r_{\text{t}}\right)$	Cost $\left(B\right)$	Depreciation $d_{\text{t}}=r_{\text{t}}\times B$
$1$	$14.29\%$	$\$20,000$	$\$7,145$
$2$	$24.49\%$	$\$20,000$	$\$12,245$
$3$	$17.49\%$	$\$20,000$	$\$8,745$
$4$	$12.49\%$	$\$20,000$	$\$6,245$
$5$	$8.93\%$	$\$20,000$	$\$4,465$
$6$	$8.92\%$	$\$20,000$	$\$4,460$
$7$	$8.93\%$	$\$20,000$	$\$4,465$
$8$	$4.46\%$	$\$20,000$	$\$2,230$

To determine

(b)

The depreciation schedule using straight line depreciation.

Answer to Problem 16P

The depreciation schedule using straight line depreciation is shown below.

Year $\left(t\right)$	Depreciation $d_{\text{t}}=\frac{B-S}{n}$
$1$	$\$5,000$
$2$	$\$5,000$
$3$	$\$5,000$
$4$	$\$5,000$
$5$	$\$5,000$
$6$	$\$5,000$
$7$	$\$5,000$
$8$	$\$5,000$

Explanation of Solution

Concept used:

Write the expression to calculate the depreciation value for the crystal extraction device

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

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

Calculation:

Calculate the depreciation for the crystal extraction device.

Substitute $\$50,000$ for $B$, $\$10,000$ for $S$ and $8$ for $n$ in Equation (II).

$\begin{array}{c}{d}_{\text{t}}=\frac{\$50,000-\$10,000}{8}\\ =\$5,000\end{array}$

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

Year $\left(t\right)$	Depreciation $d_{\text{t}}=\frac{B-S}{n}$
$1$	$\$5,000$
$2$	$\$5,000$
$3$	$\$5,000$
$4$	$\$5,000$
$5$	$\$5,000$
$6$	$\$5,000$
$7$	$\$5,000$
$8$	$\$5,000$

Conclusion:

The depreciation schedule using straight line depreciation is shown below.

Year $\left(t\right)$	Depreciation $d_{\text{t}}=\frac{B-S}{n}$
$1$	$\$5,000$
$2$	$\$5,000$
$3$	$\$5,000$
$4$	$\$5,000$
$5$	$\$5,000$
$6$	$\$5,000$
$7$	$\$5,000$
$8$	$\$5,000$

To determine

(c)

The depreciation schedule using SOYD.

Answer to Problem 16P

The depreciation schedule using SOYD is shown below.

Year $\left(t\right)$	Depreciation $\left(d_{\text{t}}\right)$
$1$	$\$8,888.88$
$2$	$\$7,778$
$3$	$\$6,667$
$4$	$\$5,556$
$5$	$\$4,444$
$6$	$\$3,333$
$7$	$\$2,222$
$8$	$\$1,111$

Explanation of Solution

Concept used:

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

Write the expression to calculate the depreciation of the crystal extraction device.

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

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

Calculation:

Calculate the depreciation using SOYD for the crystal extraction device.

Substitute $8$ for $n$, $\$50,000$ for $B$ and $\$10,000$ for $S$ in Equation (III).

$\begin{array}{c}{d}_{\text{t}}=\frac{8-t+1}{\left[\frac{8\left(8+1\right)}{2}\right]}\left(\$50,000-\$10,000\right)\\ =\frac{\left(9-t\right)}{36}\times \left(\$40,000\right)\\ =\$1111.11\left(9-t\right)\end{array}$ ......(IV)

Calculate the depreciation value for 5 year.

Year $\left(t\right)$	Depreciation $\left(d_{\text{t}}\right)$
$1$	$\$8,888.88$
$2$	$\$7,778$
$3$	$\$6,667$
$4$	$\$5,556$
$5$	$\$4,444$
$6$	$\$3,333$
$7$	$\$2,222$
$8$	$\$1,111$

Here, the depreciation is calculated from Equation (IV).

Conclusion:

The depreciation schedule using SOYD is shown below.

Year $\left(t\right)$	Depreciation $\left(d_{\text{t}}\right)$
$1$	$\$8,888.88$
$2$	$\$7,778$
$3$	$\$6,667$
$4$	$\$5,556$
$5$	$\$4,444$
$6$	$\$3,333$
$7$	$\$2,222$
$8$	$\$1,111$

To determine

(d)

The depreciation schedule using double declining balance depreciation.

Answer to Problem 16P

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

Year $\left(t\right)$	Depreciation $\left(d_{\text{t}}\right)$
$1$	$\$12,500$
$2$	$\$9,375$
$3$	$\$7,031$
$4$	$\$5,273.5$
$5$	$\$3,955.125$
$6$	$\$2,966.35$
$7$	$\$2,224.75$
$8$	$\$1,668.56$

Explanation of Solution

Concept used:

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

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

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

Calculation:

Calculate the depreciation of the crystal extraction device for the first year.

Substitute $8$ for $n$, $\$50,000$ for $B$ and $0$ for depreciation charge up to year $t$ in Equation (V).

$\begin{array}{c}{d}_{\text{t}}=\frac{2}{8}\left(\$50,000-\$0\right)\\ =\frac{2}{8}\times \$50,000\\ =\$12,500\end{array}$

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

Year $\left(t\right)$	Depreciation charge up to year $t$	Depreciation $\left(d_{\text{t}}\right)$
$1$	$0$	$\$12,500$
$2$	$\$12,500$	$\$9,375$
$3$	$\$21,875$	$\$7,031$
$4$	$\$28,906$	$\$5,273.5$
$5$	$\$34,179.5$	$\$3,955.125$
$6$	$\$38,134.625$	$\$2,966.35$
$7$	$\$41,101$	$\$2,224.75$
$8$	$\$43,325.75$	$\$1,668.56$

Conclusion:

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

Year $\left(t\right)$	Depreciation $\left(d_{\text{t}}\right)$
$1$	$\$12,500$
$2$	$\$9,375$
$3$	$\$7,031$
$4$	$\$5,273.5$
$5$	$\$3,955.125$
$6$	$\$2,966.35$
$7$	$\$2,224.75$
$8$	$\$1,668.56$