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Contemporary Engineering Economics
Depreciation Methods Lecture No. 31 Chapter 9 Contemporary Engineering Economics Copyright © 2016
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Book Depreciation Methods
Purpose: Used in reporting net income to stockholders/investors Types of Depreciation Methods Straight-line method Declining balance method Unit production method
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Straight-Line (SL) Method
Principle: A fixed asset as providing its service in a uniform fashion over its life Formula Annual depreciation Dn = (I − S) / N, and constantfor all n. Book value Bn = I − n (D) where I = cost basis S = Salvage value N = depreciable life Example: I = $10,000 S= $2,000 N= 5 years
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Declining Balance (DB) Method
Principle: A fixed asset as providing its service in a decreasing fashion Formula Example: I = $10,000 S = $778 N = 5 years α = 0.40 where 0 <α<2(1/N)
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Example 9.5: DB Switching to SL
Given: Depreciation Base =$10,000 Salvage Value = 0 Depreciation rate = 200% DB Depreciable life = 5 years Find: When switching to SL Without Switching SL Dep. Rate = 1/5 α = (200%) (1/5) = 0.40 Note: Without switching, we have not depreciated the entire cost of the asset and thus have not taken full advantage of depreciation’s tax deferring benefits.
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Case 1: S<BN Switch from DB to SL after n’ Example: S = 0
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Case 2: S>BN No further depreciation after n” Example: S = $2,000
Note: Tax law does not permit a business to depreciate assets below their salvage value.
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Units-of-Production Method
Given: I = $55,000, S = $5,000, total service unit = 250,000 miles, service units consumed = 30,000 miles Find: Dn Solution: Principle: Service units will be consumed in a non-time-phased fashion. Formula: I = Initial investment S = Salvage value
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Tax Depreciation Purpose: To determine the income taxes owed for the IRS Assets placed in service prior to 1981 Used the book depreciation methods (SL, DB, SOYD) Assets placed in service from 1981 to 1986 Used the ACRS (Accelerated Cost Recovery System) Table Assets placed in service from 1986 to present Used the MACRS (Modified ACRS) Table
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Modified Accelerated Cost Recovery Systems (MACRS)
Personal Property Depreciation schedule based on the DB method switching to SL Half-year convention Zero salvage value Real Property SL Method Mid-month convention
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MACRS Depreciation Schedules for Personal Property with Half-Year Convention
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Comparison Between DDB with Switching to SL and MACRS Method
Conventional DDB Method Cost basis: $10,000 Salvage value: $0 Depreciable life: 5 years DB rate: 200% MACRS Method Property class: 5-year Half-year convention Figure: 09-05EXM
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MACRS for Real Property
Types 27.5-year (residential) 39-year (commercial) SL Method Mid-month convention Zero salvage value Example: Placed a residential property in service in March. Find the depreciation allowance in year 1. D1 = (9.5/12)(100%/27.5) = %
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Depletion Depletion is the physical reduction of natural resources (not time-phased). Two types of depletion Cost depletion Percentage depletion
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Cost Depletion Concept: Units-of-production method
Cost depletion formula Example: Cost basis = $120,000, Total recoverable volume = 1.5MBF Amount sold this year = 0.5 MBF Allowed depletion this year?
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Percentage Depletion Solution
Concept: Based on a prescribed percentage of the gross income from the property during the tax year Example 9.11 Given: Basis = $30 million, Total recoverable volume = 120,000 ounces of gold, Amount sold this year = 18,000 ounces, Gross income = $16,425,000, Depletion expenses = $12,250,000 Find: Maximum depletion allowance Solution
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Calculating the Allowable Depletion Deduction for Federal Tax
$2,463,750 $2,088,000 Figure: 09-06 $2,088,000 $4,500,000
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Summary Because it employs accelerated methods of depreciation and shorter-than-actual depreciable lives, the MACRS (Modified Accelerated Cost Recovery System) gives taxpayers a break: It allows them to take earlier and faster advantage of the tax-deferring benefits of depreciation. The total amount of taxes to pay remains unchangedregardless of depreciation methods adopted. It only changes the timing of the payment.
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Summary Many firms select straight-line depreciation for book depreciation because of its relative ease of calculation. Given the frequently changing nature of depreciation and tax law, we must use whatever percentages, depreciable lives, and salvage values mandated at the time an asset is acquired.
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