Question

Computing first-year depreciation and book value

On January 1, 2018, Air Canadians purchased a used airplane for \(37,000,000. Air Canadians expects the plane to remain useful for five years (4,000,000 miles) and to have a residual value of \)5,000,000. The company expects the plane to be flown 1,400,000 miles during the first year.

Requirements

1. Compute Air Canadians’s first-year depreciation expense on the plane using the following methods:

a. Straight-line

b. Units-of-production

c. Double-declining-balance

2. Show the airplane’s book value at the end of the first year for all three methods.

Short answer

Depreciation	Value at end of the first year
$6,400,000	$30,600,000
$11,200,000	$25,800,000
$14,800,000	$22,200,000

Step-by-step solution

Definition of Straight Line Method

The method of calculating depreciation under which each year of the asset's useful life reports the same depreciation is known as the straight-line method. The depreciation method under this method is calculated using salvage value, cost, and useful life.

Calculation of depreciation

a. Straight line

$\begin{array}{rcl}Depreciation& =& \frac{Cost-Salvagevalue}{Estimatedusefullifeinyears}\\ & =& \frac{\$37,000,000-\$5,000,000}{5}\\ & =& \$6,400,000\end{array}$

b. Units of production method

$\begin{array}{rcl}Depreciation& =& \frac{Cost-Salvagevalue}{Estimatedusefullifeinmiles}\times Milesrunduringfirstyear\\ & =& \frac{\$37,000,000-\$5,000,000}{4,000,000}\times 1,400,000\\ & =& \$11,200,000\end{array}$

c. Double-declining method:

$\begin{array}{rcl}Depreciation& =& Cost\times \frac{100\%}{Usefullife}\times 2\\ & =& \$37,000,000\times \frac{100\%}{5}\times 2\\ & =& \$37,000,000\times 20\%\times 2\\ & =& \$14,800,000\end{array}$

Book value at the end of the first year

Method	Book value	-	Depreciation	=	Value at end of the first year
Straight line	$37,000,000	-	$6,400,000	=	$30,600,000
Units of production	$37,000,000	-	$11,200,000	=	$25,800,000
Double declining method	$37,000,000	-	$14,800,000	=	$22,200,000