Chapter 11, Problem 10P

To determine

(a)

The depreciation schedule using straight line depreciation.

Answer to Problem 10P

The depreciation schedule using straight line depreciation is shown below.

Year $\left(t\right)$	Depreciation $d_{\text{t}}=\frac{B-S}{n}$
$1$	$\$15,200$
$2$	$\$15,200$
$3$	$\$15,200$
$4$	$\$15,200$
$5$	$\$15,200$

Explanation of Solution

Given:

The cost of the capsulating machine is $\$76,000$.

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

Concept used:

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

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

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

Calculation:

Calculate the depreciation for capsulating machine.

Substitute $\$76,000$ for $B$, $0$ for $S$ and $5$ for $n$ in Equation (I).

$\begin{array}{c}{d}_{\text{t}}=\frac{\$76,000-0}{5}\\ =\$15200\end{array}$

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

Year $\left(t\right)$	Depreciation $d_{\text{t}}=\frac{B-S}{n}$
$1$	$\$15,200$
$2$	$\$15,200$
$3$	$\$15,200$
$4$	$\$15,200$
$5$	$\$15,200$

Conclusion:

The depreciation schedule using straight line depreciation is shown below.

Year $\left(t\right)$	Depreciation $d_{\text{t}}=\frac{B-S}{n}$
$1$	$\$15,200$
$2$	$\$15,200$
$3$	$\$15,200$
$4$	$\$15,200$
$5$	$\$15,200$

To determine

(b)

The depreciation schedule using SOYD.

Answer to Problem 10P

The depreciation schedule using SOYD is shown below.

Year $\left(t\right)$	Depreciation $\left(d_{\text{t}}\right)$
$1$	$\$25,333.33$
$2$	$\$20,266.67$
$3$	$\$15,200$
$4$	$\$10,133.33$
$5$	$\$5,066.67$

Explanation of Solution

Concept used:

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

Write the expression to calculate the depreciation of the capsulating machine.

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

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

Calculation:

Calculate the depreciation using SOYD for the capsulating machine.

Substitute, $5$ for $n$, $\$76,000$ for $B$ and $\$0$ for $S$ in Equation (II)

$\begin{array}{c}{d}_{\text{t}}=\frac{5-t+1}{\left[\frac{5\left(5+1\right)}{2}\right]}\left(\$76,000-\$0\right)\\ =\frac{\left(6-t\right)}{15}\times \left(\$76,000\right)\\ =\$5066.67\left(6-t\right)\end{array}$ ...... (III)

Calculate the depreciation value for 5 year.

Year $\left(t\right)$	Depreciation $\left(d_{\text{t}}\right)$
$1$	$\$25,333.33$
$2$	$\$20,266.67$
$3$	$\$15,200$
$4$	$\$10,133.33$
$5$	$\$5,066.67$

Here, calculate the depreciation from Equation (III).

Conclusion:

The depreciation schedule using SOYD is shown below.

Year $\left(t\right)$	Depreciation $\left(d_{\text{t}}\right)$
$1$	$\$25,333.33$
$2$	$\$20,266.67$
$3$	$\$15,200$
$4$	$\$10,133.33$
$5$	$\$5,066.67$

To determine

(c)

The depreciation schedule using double declining balance depreciation.

Answer to Problem 10P

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

Year $\left(t\right)$	Depreciation $\left(d_{\text{t}}\right)$
$1$	$\$30,400$
$2$	$\$18,240$
$3$	$\$10,944$
$4$	$\$6,566.40$
$5$	$\$9,849.60$

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 capsulating machine for the first year.

Substitute, $5$ for $n$, $\$76,000$ for $B$ and $0$ for depreciation charge up to year $t$ in Equation (IV)

$\begin{array}{c}{d}_{\text{t}}=\frac{2}{5}\left(\$76,000-\$0\right)\\ =\frac{2}{5}\times \$76,000\\ =\$30,400\end{array}$

Similarly calculate the depreciation of the capsulating machine for 5 years and enter it in a table below.

Year $\left(t\right)$	Depreciation charge up to year $t$	Depreciation $\left(d_{\text{t}}\right)$
$1$	$0$	$\$30,400$
$2$	$\$30,400$	$\$18,240$
$3$	$\$48,640$	$\$10,944$
$4$	$\$59,584$	$\$6,566.40$
$5$	$\$66,150.40$	$\$9,849.60$

Conclusion:

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

Year $\left(t\right)$	Depreciation $\left(d_{\text{t}}\right)$
$1$	$\$30,400$
$2$	$\$18,240$
$3$	$\$10,944$
$4$	$\$6,566.40$
$5$	$\$9,849.60$