Question

Apex Fitness Club uses straight-line depreciation for a machine costing \(23,860, with an estimated four-year life and a \)2,400 salvage value. At the beginning of the third year, Apex determines that the machine has three more years of remaining useful life, after which it will have an estimated $2,000 salvage value. Compute (1) the machine’s book value at the end of its second year and (2) the amount of depreciation for each of the final three years given the revised estimates.

Short answer

1. The machine’s book value at the end of its second year is $13,130.
2. The amount of the depreciation for each of the final three years is $3,710.

Step-by-step solution

Formula of revised depreciation

$\mathbf{Revised} \mathbf{depreciation}=\frac{\mathbf{book}\mathbf{value}-\mathbf{revised} \mathbf{salvage} \mathbf{value}}{\mathbf{revised} \mathbf{remaining} \mathbf{useful} \mathbf{life}}.$

Computation of revised depreciation

Depreciation before change in estimate:

$\begin{array}{rcl}Depreciation& =& \frac{\$23,860-\$2,400}{4}\\ & =& \frac{\$21,460}{4}\\ & =& \$5,365.\end{array}$

Depreciation after change in estimate:

$\begin{array}{rcl}Depreciation& =& \frac{\$23,860-\$12,730}{3}\\ & =& \frac{\$11,130}{3}\\ & =& \$3,710.\end{array}$

Note:

$\begin{array}{rcl}\mathbf{Salvage}\mathbf{}\mathbf{ }\mathbf{value}& \mathbf{=}& \mathbf{accumulated}\mathbf{}\mathbf{ }\mathbf{ }\mathbf{depreciation}\mathbf{ }\mathbf{}\mathbf{of}\mathbf{ }\mathbf{ }\mathbf{}\mathbf{2}\mathbf{}\mathbf{years}\mathbf{+}\mathbf{revised}\mathbf{}\mathbf{ }\mathbf{salvage}\mathbf{ }\mathbf{}\mathbf{value}\\ & \mathbf{=}& \mathbf{\$}\mathbf{10}\mathbf{,}\mathbf{730}\mathbf{+}\mathbf{\$}\mathbf{2000}\mathbf{=}\mathbf{\$}\mathbf{12}\mathbf{,}\mathbf{730}\mathbf{.}\end{array}$

Tabular representation

Year	Book value at beginning	Depreciation expense	Book value
1	$23,860	$5,365	$18,495
2	$18,495	$5,365	$13,130
3	$13,130	$3,710	$9,420
4	$9,420	$3,710	$5,710
5	$5,710	$3,710	$2,000 (Salvage value)