Study Guide
Chapter 7 Depreciation and Income Taxes
-
University:
Michigan State University -
Course:
EC 301 | Intermediate Microeconomics Academic year:
2024
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Views:
291
Pages:
17
Author:
Dixie Summers
Chapter 7: Depreciation and
Income Taxes Depreciation
Depreciation
Accounting concept (noncash or book cost).
Measures the decrease in value of physical properties with time and
use.
Begins once the property is placed in service for business.
Depreciable properties
Tangible properties (machinery, vehicles, furniture, buildings).
Intangible properties (patents, copyrights, franchises). Depreciation methods
Time
Straight line (SL)
method
Sum of years
digits (SOYD)
method
Use
Declining
balance (DB)
method
Units of
production
method Straight line (SL) method
- Constant amount is depreciated each year over the depreciable (useful) life.
Where: Example
A tool has a cost basis of $200,000 and a five-year depreciable life. The estimated salvage
value is $20,000 at the end of five years. Determine the annual depreciation using SL method
and tabulate the annual depreciation amounts and book values at the end of each year. Sum of years digits (SOYD) method
- This method accelerates the recognition of depreciation (most depreciation is recognized in the
first few years of the asset’s life).
Example: a property has a cost basis of $33,000 and a salvage value of $3,000 with a 5-year useful life. Use the
SOYD method to determine the annual depreciations and book values at end of each year. Declining balance (DB) method
- Also called constant-percentage method or Matheson formula.
- Annual depreciation is a fixed percentage of the BV at the beginning of the year.
Where:
R: constant percentage ratio = 2/𝑁𝑁 when 200% DB is being used (double declining balance – DDB) and
1.5/𝑁𝑁 when 150% DB is used. Example – DB method
A new cutting machine has a cost basis of $4,000 and a 10-year depreciable life. The machine
has no market value at the end of its life. Use the DB method to calculate the annual
depreciation when:
(a) 𝑅𝑅 = 2/𝑁𝑁 (200% DB or DDB).
(b) 𝑅𝑅 = 1.5/𝑁𝑁 (150% DB). Example – cont’d
200% DB method only
0
1
2
3
4
5
6
7
8
9
10
$800
$640
$512
$409.6
$327.68
$262.14
$209.72
$167.77
$134.22
$107.37
$4,000
$3,200
$2,560
$2,048
$1,638.4
$1,310.72
$1,048.58
$838.86
$671.09
$536.87
$429.50
Never
reaches SV
Switchover to SL method
- Switchover occurs in the year in which the SL depreciation is greater than or
equal to the DB depreciation. Example – cont’d
200% DB method only
1
2
3
4
5
6
7
8
9
10
11
$4,000
$3,200
$2,560
$2,048
$1,638.4
$1,310.72
$1,048.58
$786.44
$524.30
$262.14
0
$800
$640
$512
$409.6
$327.68
$262.14
$209.72
$167.77
$134.22
$107.37
Switch
$400
$355.56
$320
$292.57
$273.07
$262.14
$262.14
$262.14
$262.14
$262.14
$800
$640
$512
$409.6
$327.68
$262.14
$262.14
$262.14
$262.14
$262.14
*** 𝑑𝑑𝑘𝑘 SL method is calculated based on the BV @ beginning of each year, SV, and the remaining years. Units of production method
- Decrease in value is a function of use.
Example: An equipment has a basis of $50,000 and is expected to have a $10,000
SV when replaced after 30,000 hours of use. Find the depreciation rate per hour
of use and find its book value after 10,000 hours of operation. Taxes
Types of taxes
Income taxes: function of gross revenue minus allowable deductions.
Property taxes: function of the property (e.g., land, building,
equipment, etc.) value (independent of income or profit).
Sales taxes: function of the value of purchased goods or services
(independent of income or profit).
Excise taxes: taxes imposed on the purchase of non-necessities
(independent of income or profit). After-tax analysis
After-tax MARR ≅ Before-tax MARR × (1 – effective income tax rate)
Taxable income = Gross income – All expenses (except capital
investment) – Depreciation deductions
Example: A company generates $1,500,000 of gross income during its tax year
and incurs operating expenses of $800,000. Property taxes on business assets
amount to $48,000. The total depreciation deductions for the tax year equal
$114,000. What is the taxable income of this firm?
Taxable income = $1,500,000 − $800,000 − $48,000 − $114,000 = $538,000. After-tax cash flow (ATCF)
After-tax economic analysis is the same as before-tax analysis except:
Taxable income
Before-tax cash flow Example
A new equipment is estimated to cost $180,000 and is expected to reduce net annual expenses by $36,000 for
10 years and to have a $30,000 market value at the end of the 10th year. Using the SL depreciation method, and
assuming a 40% effective income tax rate, develop the ATCF and BTCF.
=
EOY 𝒌𝒌
0
1
2
3
4
5
6
7
8
9
10
10*
Capital
-$180,000
-
𝑹𝑹𝐤𝐤
$36,000
$36,000
$36,000
$36,000
$36,000
$36,000
$36,000
$36,000
$36,000
$36,000
$30,000
𝑬𝑬𝒌𝒌
-
$180,000 − $30,000
10
BTCF
-$180,000
$36,000
$36,000
$36,000
$36,000
$36,000
$36,000
$36,000
$36,000
$36,000
$36,000
$30,000
𝒅𝒅𝒌𝒌
$15,000
$15,000
$15,000
$15,000
$15,000
$15,000
$15,000
$15,000
$15,000
$15,000
-
= BTCF − 𝑑𝑑𝑘𝑘
= −𝑡𝑡 × taxable income
Taxable income Income tax
$21,000
$21,000
$21,000
$21,000
$21,000
$21,000
$21,000
$21,000
$21,000
$21,000
0
-$8,400
-$8,400
-$8,400
-$8,400
-$8,400
-$8,400
-$8,400
-$8,400
-$8,400
-$8,400
0
= BTCF + income tax
ATCF
-$180,000
$27,600
$27,600
$27,600
$27,600
$27,600
$27,600
$27,600
$27,600
$27,600
$27,600
$30,000 Example
A company wants to purchase a machine with an initial cost of $100,000 with
additional $10,000 installation and transportation costs and a salvage value
after 10 years of $10,000. If the annual revenue is $20,000 and the annual
expenses are $5,000, and using the SL depreciation method and a 30% income
tax rate:
- What is the BTCF for the 3rd year?
- What is the ATCF for the 2nd year? Example
Assume the cost basis is $35,000, annual revenue is $30,000, annual expenses
are $13,000 in the first year and increasing by $1,000 per year. The useful life is
4 years and the SOYD is the applicable depreciation method, develop BTCFs and
ATCFs using a 15% income tax rate.
Chapter 7 Depreciation and Income Taxes
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