1. Contemporary Engineering Economics
Depreciation Methods
Lecture No. 31
Chapter 9
Contemporary Engineering Economics
Copyright © 2016

2. 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

3. 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

4. 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)

5. 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.

6. Case 1: S<BN
Switch from DB to SL after n’
Example: S = 0

7. 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.

8. 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

9. 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

10. 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

11. MACRS Depreciation Schedules for Personal Property with Half-Year Convention

12. 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

13. 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)
= %

14. Depletion
Depletion is the physical reduction of natural resources (not time-phased).
Two types of depletion
Cost depletion
Percentage depletion

15. 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?

16. 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

17. Calculating the Allowable Depletion Deduction for Federal Tax
$2,463,750
$2,088,000
Figure: 09-06
$2,088,000
$4,500,000

18. 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.

19. 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.