Question

Problem #3 (a) Using straight-line depreciation, what is the book value after 5 years for an asset costing $100,000 that has a salvage value of 20,000 after 10 years? What is the depreciation charge in the 9th year? (b) Using decline-balance depreciation with d=15%, what is the book value after 4 years for an asset costing $250,000? What is the depreciation charge in the 5th year? (c) What is the depreciation rate using declining-balance for an asset costing $250,000 and having a salvage value of $20,000 after 10 years? Problem #4: Textbook Problem 2.42 A machine costs $500,000 and has a planned life of 30 years, with a salvage value of $50,000 (at the end of 30 years) using straight-line depreciation. What depreciation rate will result in the same book values, for both the declining-balance and straight-line methods at the end of year 20?

Answer 1

Problem #3 :

a) Straight line depreciation:

Staight line depreciation is a simple method for calculating how much a particular fixed asset depreciates over a period of time.

First we will arrive annual depreciation.

Formula for annual depreciation.

Annual Depreciation = (Purchase price - Salvage value ) / Useful life.

Annual Depreciation = $8,000 {($100,000 - $20,000 )/10}

Depreciation table using Straight line method is as below.

N 3 Closing Opening Book Year Book Value Depreciation Value 1 $100,000 $8,000 $92,000 $92,000 $8,000 $84,000 31 $84,000 $8,000 $76,000 4 $76,000 $8,000 $68,000 5 $68,000 $8,000 $60,000 61 $60,000 $8,000 $52,000 7 $52,000 $8,000 $44,000 8 $44,000 $8,000 $36,000 9 $36,000 $8,000 $28,000 10 $28,000 $8,000 $20,000 5 6 8

Book value after 5 years is $60,000.

Depreciation charge in 9th year is $8,000.

b) Decline balance depreciation:

Depreciation expense under the declining balance is calculated by applying the depreciation rate to the book value of the asset at the start of the period.

In this method, Depreciation will decrease with age of asset.

Year Closing Opening Depreciation Book Book Value @ 15% Value 11 $250,000 $37,500 $212,500 2 $212,500 $31,875 $180,625 3 $180,625 $27,094 $153,531 4 $153,531 $23,030 $130,502 5 $130,502 $19,575 $110,926 3

Book Value after 4 years is $130,502.

Depreciation for the th year $19,575.

C) Depreciation rate using declining balance:

Formula for Depreciation rate for declining balance.

Depreciation rate = 1- [salvage value/Cost vaue]^1/useful life

Depreciation rate = 1-[$20,000/$250,000]^1/10

Depreciation rate = 1-0.08^0.10

Depreciation rate = 22.32%

Closing Opening Depreciation Book Year Book Value @ 22.32% Value 11 $250,000 $55,800 $194,200 2 $194,200 $43,345 $150,855 3 $150,855 $33,671 $117,184 4 $117,184 $26,155 $91,028 5 $91,028 $20,318 $70,711 6 $70,711 $15,783 $54,928 7 $54,928 $12,260 $42,668) 8 $42,668 $9,524 $33,145 9 $33,145 $7,398 $25,747 10 $25,747) $5,747 $20,000

Problem #4 : Depreciation rate

Cost Value = $500,000

Salvage value =$50,000

Life of asset = 30 years

Depreciation rate for straight line = ( Cost value - Slavage value ) / Cost of asset.

Depreciation rate for 30 years = 3% ($500,000-$50,000)/$500,000.

Depreciation rate for declining balance method for 20 years.

Depreciation rate = 1- [salvage value/Cost vaue]^1/useful life

Depreciation rate = 1-[$50,000/$500,000]^1/30

Depreciation rate = 1-0.1^0.03333

Depreciation rate = 7.39% ( Round off to 7.4%)

Note : Depreciation rate in declining method is same during life time of asset.

Hence depreciation rate at the end of 20 years is 7.39% (Round off to 7.4%)

Depreciation rate for straight line method for 20 years.

Depreciation amount charged in staight line method per year = $15,000 ($500,000-$50,000)/30

Formula for depreciation under straight line method = Depreciation charged / Book value end of 20 years

Book value end of 20 years

Depreciation charged for 20 years = $300,000 ($15,000*20)

Book value end of 20 years = $200,000 ( $500,000-$300,000)

Depreciation rate = 7.5% ($15,000/$200,000).

Depreciation rate for straight line method at the end of 20 years = 7.5%.