Chapter 11, Problem 3P

To determine

The depreciation table.

Answer to Problem 3P

The depreciation table is shown below

Year $\left(t\right)$	MACRS $\left(r_{\text{t}}\right)$	Cost $\left(B\right)$	Depreciation $d_{\text{t}}=r_{\text{t}}\times B$	CumulativeDepreciation $\left(Cu{m}_{d_{\text{t}}}\right)$	Book value at the end of the year $BV=B-Cu{m}_{d_{\text{t}}}$
$1$	$14.29\%$	$\$25,000$	$\$3,573$	$\$3,573$	$\$21,428$
$2$	$24.49\%$	$\$25,000$	$\$6,123$	$\$9,695$	$\$15,305$
$3$	$17.49\%$	$\$25,000$	$\$4,373$	$\$14,068$	$\$10,933$
$4$	$12.49\%$	$\$25,000$	$\$3,123$	$\$17,190$	$\$7,810$
$5$	$8.93\%$	$\$25,000$	$\$2,233$	$\$19,423$	$\$5,578$
$6$	$8.92\%$	$\$25,000$	$\$2,230$	$\$21,653$	$\$3,348$
$7$	$8.93\%$	$\$25,000$	$\$2,233$	$\$23,885$	$\$1,115$
$8$	$4.46\%$	$\$25,000$	$\$1,115$	$\$25,000$	$\$0$
Total			$\$25,000$

Explanation of Solution

Given:

Cost of the printing machine is $\$25,000$.

Time period is $7\text{years}$.

Concept used:

Write the expression to calculate the depreciation value for the printing machine.

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

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

Write the expression to calculate the book value at the end of the year.

$BV=B-Cu{m}_{d_{\text{t}}}$ ...... (II)

Here, book value at the end of the year is $BV$, cost of the printing machine is $B$, and the cumulative depreciation is $Cu{m}_{d_{\text{t}}}$.

Calculation:

The given asset comes under MACRS “office equipment” designation. Thus it is considered as a 7 year property. Using MACRS GDS 7 year property table calculate the depreciation and the book value for the printing machine.

Calculate the depreciation for printing machine.

Substitute $\$25,000$ for $B$ and $14.29\%$ for $r_{\text{t}}$ in Equation (I).

$\begin{array}{c}{d}_{\text{t}}=\$25,000\times 14.29\%\\ =\$3572.5\end{array}$

Calculate the book value at the end of the year.

Substitute $\$25,000$ for $B$ and $\$3,573$ for $Cu{m}_{d_{\text{t}}}$ in Equation (II).

$\begin{array}{c}BV=\$25,000-\$3,573\\ =\$21,427\end{array}$

Calculate the depreciation and book value for all the 7 years and enter them in a table below.

Year $\left(t\right)$	MACRS $\left(r_{\text{t}}\right)$	Cost $\left(B\right)$	Depreciation $d_{\text{t}}=r_{\text{t}}\times B$	CumulativeDepreciation $\left(Cu{m}_{d_{\text{t}}}\right)$	Book value at the end of the year $BV=B-Cu{m}_{d_{\text{t}}}$
$1$	$14.29\%$	$\$25,000$	$\$3,573$	$\$3,573$	$\$21,428$
$2$	$24.49\%$	$\$25,000$	$\$6,123$	$\$9,695$	$\$15,305$
$3$	$17.49\%$	$\$25,000$	$\$4,373$	$\$14,068$	$\$10,933$
$4$	$12.49\%$	$\$25,000$	$\$3,123$	$\$17,190$	$\$7,810$
$5$	$8.93\%$	$\$25,000$	$\$2,233$	$\$19,423$	$\$5,578$
$6$	$8.92\%$	$\$25,000$	$\$2,230$	$\$21,653$	$\$3,348$
$7$	$8.93\%$	$\$25,000$	$\$2,233$	$\$23,885$	$\$1,115$
$8$	$4.46\%$	$\$25,000$	$\$1,115$	$\$25,000$	$\$0$
Total			$\$25,000$

Conclusion:

The depreciation table is shown below.

Year $\left(t\right)$	MACRS $\left(r_{\text{t}}\right)$	Cost $\left(B\right)$	Depreciation $d_{\text{t}}=r_{\text{t}}\times B$	CumulativeDepreciation $\left(Cu{m}_{d_{\text{t}}}\right)$	Book value at the end of the year $BV=B-Cu{m}_{d_{\text{t}}}$
$1$	$14.29\%$	$\$25,000$	$\$3,573$	$\$3,573$	$\$21,428$
$2$	$24.49\%$	$\$25,000$	$\$6,123$	$\$9,695$	$\$15,305$
$3$	$17.49\%$	$\$25,000$	$\$4,373$	$\$14,068$	$\$10,933$
$4$	$12.49\%$	$\$25,000$	$\$3,123$	$\$17,190$	$\$7,810$
$5$	$8.93\%$	$\$25,000$	$\$2,233$	$\$19,423$	$\$5,578$
$6$	$8.92\%$	$\$25,000$	$\$2,230$	$\$21,653$	$\$3,348$
$7$	$8.93\%$	$\$25,000$	$\$2,233$	$\$23,885$	$\$1,115$
$8$	$4.46\%$	$\$25,000$	$\$1,115$	$\$25,000$	$\$0$
Total			$\$25,000$