Chapter 8

Depreciation

Definition:

Depreciation is the reduction in value of an asset over

time.

Depreciation represents the loss in value due to:

– Use, and wear and tear on the asset

– Deterioration over time

– Obsolescence

– Technological replacement

Depreciation terms

Depreciation is important because it affects the tax that firms pay.

TAX = (PROFIT – COSTS) (TAX RATE)

COSTS = EXPENSES + DEPRECIATION

Depreciation is a deduction from taxable income.

Obviously, a well-run firm wants to choose the depreciation method that will minimize its taxable income.

To do so, the firm owner/employees must understand how the depreciation methods work.

Depreciation terms

Depreciation terms

Depreciation: Example A firm has $1,000,000 of taxable income. If its tax rate is 25%, it would pay $250,000 in taxes ignoring

depreciation.

If it can deduct $50,000 in depreciation charges, its net taxable income is $950,000.

Thus, it would pay taxes of 0.25 (950,000) = $237,500.

Depreciation saves 250,000 – 237,500 = 0.25(50,000) = 12,500. If it could deduct more than $50,000 it would pay even less taxes.

Unlike other real expenses, depreciation is not an actual cash flow amount.

Two types of depreciation used by corporations Book depreciation -- Use by a corporation for internal financial accounting

Tax depreciation -- Use in tax calculations for government regulations.

Depreciation terms

Depreciation: Requirements

In general business assets can only be depreciated if they meet the following basic requirements:

The property must be used for business purposes to produce income

The property must have a useful life that can be determined, and this life must be longer than one year

The property must be an asset that decays, gets used up, wears out, becomes obsolete, or loses value to the owner from natural causes

Depreciation terms

Cost Item Type of Cost Reason

Pizza dough, toppings

Delivery van

Employee wages

Furnishings for dining room

New baking oven

Utilities for refrigerator

Example: Joe runs a pizza restaurant. He classifies some of his costs as follows.

Expense

Depreciation

Expense

Depreciation

Depreciation

Expense

Life < 1 yr, loses value immediately

Meets 3 depreciation requirements

Life < 1 yr, loses value immediately

Meets 3 depreciation requirements

Meets 3 depreciation requirements

Life < 1 yr, loses value immediately

1. Must be used for business purposes to produce income

2. Must have a useful life that can be determined, and this life must be longer than one year

3. Must be an asset that decays, gets used up, wears out, becomes obsolete, or loses value to the owner from natural causes

Depreciation terms

Classes of Business Property Tangible property can be seen, touched, and felt.

– Real property includes real estate and its improvements, such as, buildings, factories, other construction

– Personal property Income-producing, tangible property of a corporation, e.g., vehicles, equipment, etc.

Intangible property is all property that has value to the owner but cannot be directly seen or touched. Examples include patents, trademarks, trade names, and franchises.

Depreciation terms

Examples of depreciable business assets:– Copy machines, Helicopters, Buildings, Interior furnishing,

Production equipment, Computer networks

Many different types of properties that wear out, decay, or lose value can be depreciated as business assets.

Examples of nondepreciable business assets: Land: it does not wear out, lose value, or have a determinable

useful life. Indeed, often it increases in value. Leased property: only the owner of property may claim

depreciation expenses.

Depreciation terms

Time, years

BV, $

S

Basis (First cost), B – Total cost of asset including purchase, installation fees, etc.

Recovery period, n – Depreciable life in years. Tax and book depreciation lives often vary

Salvage, S – Estimated value at end of recovery periodBook Value, BV –

Remaining, undepreciated investment after all depreciation to date is removed

Depreciation terms

.

..

Some additional terms to know Depreciation rate, d – rate for reducing the

value of assets using depreciation. (Rate is dt when it varies each year t)

Market Value - the value others would place on the property of interest.

Half-year convention – assumes asset is placed into initial service or disposed of in midyear, regardless of when it actually occurs. (Used in US-approved tax depreciation method)

Depreciation terms

Some methods used in the US and other countries

Straight Line (SL) Standard against which

other methods are compared

Book value decreases linearly over time

Declining Balance (DB) Accelerated write-off

compared to SL method Defers part of tax liability to

later in recovery period Modified Accelerated Cost

Recovery System (MACRS) Required tax depreciation

method in US since 1986

Depreciation terms

n – Recovery period in years

t – year, t = 1, 2, …, n

B – First cost or basis for

depreciation

S – Estimated salvage value at

end of recovery period

Dt – Depreciation charge for

year t

dt – Depreciation rate for year t

(d, if same each year)

BVt – Book value after t years

of depreciation

Straight Line (SL) Depreciation

Notation

1 2 … n t

S

BVt

B D1D2

Excel function to display Dt:

= SLN(B,S,n)

Straight Line (SL) Depreciation

B – S n

Dt = = (B - S) d

BVt = BVt-1 - Dt = B - t×Dt

dt = d = 1/n

Depreciation charge for year t

Book value after t years of depreciation

Depreciation rate for year t

Example 8.1: An asset has a first cost of B = $900, a useful life of n = 5 years, and a salvage value of S = $70.

Year,t Dt BVt

0 - $900

1 166 734

2 166 568

3 166 402

4 166 236

5 166 70

Initial Cost

Salvage Value

Useful Life

900

70

Book Value

1 2 3 4 5 N

Straight Line (SL) Depreciation

Dt = (B-S)/n = (900-70) / 5 = 830/5 = $166. BVt = B - t×Dt = 900 – 166 × t

Accelerated depreciation: higher depreciation charges in the early years, and gradually decreasing charges in subsequent years. More realistic reflection of an asset's actual expected benefit from the use of the asset.

Declining Balance (DB) is also called fixed percentage or uniform percentage method.

Annual depreciation Dt equals book value BVt-1 at beginning of year t (which is same as end of year t-1) times fixed rate d

Dt = BVt-1 × d

Declining Balance (DB)

Values of d are related to Straight Line depreciation rate

Straight Line (SL) Rate:d = 1 / n

Maximum Rate of DB Depreciation:

dmax = 2 / n• Known as double declining balance (DDB)• If recovery period n = 5 years, dmax = 2 / n = 0.4• 40% of book value is removed each year

150% of SL rate: d = 1.5 / n

Declining Balance (DB)

Declining Balance (DB)

Annual depreciation BVt = BVt-1 - Dt

BV0 = B

BV1 = BV0 – D1 = BV0 – BV0d= BV0 (1-d)

D1 = BV0d BV2 = BV1 – D2 = BV1 – BV1d= BV0 (1-d)2

D2 = BV1d = BV0 (1-d) d ….

BVt = BVt-1 – Dt = BVt-1 – BVt-1d= BV0 (1-d)t

Dt = BV0 d (1 - d )t-1

Annual depreciation rate for each year t, relative to first cost B, is

dt = d ×(1 - d )t-1

then, Dt = dt × B

Implied Salvage value

Implied S = BVn = B ×(1 – d)n >0

Declining Balance (DB)

Estimated S

Implied S

n

BV

Implied S

Estimated S

n

BV

kk-1

Book value plots of SL, DB and DDB

SL depreciation

DB depreciation at 150% SL rate

DDB depreciation

Declining Balance (DB)

Example 8.2: First cost, B = $80,000

Salvage value, S = $10,000

depreciable life, n = 5 years

Compare the book values for two methods:

(1) DB at 150% SL rate

(2) DDB

Declining Balance (DB)

DB rate at 150% SL rate is: d=1.5/5 = 0.3 DDB rate is: dmax = 2/5 = 0.4

BVt = B × (1 - d )t

Dt = d × BVt-1

Declining Balance (DB)

Example 8.2 (cont): B = $80,000, S = $10,000, n = 5 years DB rate at 150% SL rate is: d = 0.3

BVt = B×(1 - d )t

Dt = d × BVt-1

Example 8.2 (cont): B = $80,000, S = $10,000, n = 5 years DDB rate is: dmax = 0.4

BVt = B×(1 - d )t

Dt = d × BVt-1

Declining Balance (DB)

BV5 = B(1-d)5

= 80,000 (1-0.4)5

= 6,220.8 < 10,000

So, BV5 = 10,000

and D5 = 368.