Engineering Economy

Chapter 7: Depreciation

Lecture 13

Property is depreciable if• It is used in business or held to produce

income.• It has a determinable useful life, longer

than one year.• It is something that wears out, decays, gets

used up, becomes obsolete, or loses value from natural causes.

• It is not inventory, stock in trade, or investment property.

Depreciable property is• tangible (can be seen or touched; personal or

real) or intangible (such as copyrights, patents, or franchises).

• depreciated, according to a depreciation schedule, when it is put in service (when it is ready and available for its specific use).

Depreciation Methods

PURPOSE

Use a specific model to reduce the value of an

Asset (by depreciation)

or natural resource (by depletion)

TOPICS

• Depreciation terminology

• Straight line • Declining balance • MACRS• units-of-production

Terminology

• 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 represents the diminishing amount of capital invested in the asset

• Deprecation represents an amount of money charged against future income produced by the asset

Terminology

• In most countries, depreciation is a tax deductible expense. It reduces tax liability for a corporation

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

Two types of depreciation used by corporations

Book depreciation -- Used internal to the corporation for financial and accounting purposes

Tax depreciation -- Per government regulations, used in calculating income taxes due

In an economic analysis, tax depreciation is usually concentrated upon

Terminology

Time, years

BV, $

SV

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

Book Value, BV – Remaining, undepreciated investment after all depreciation to date is removed

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

Salvage, SV – Estimated market value at end of recovery period

TerminologySome additional terms to

know

• Depreciation rate, d – fraction of first cost removed each year. (Rate is dt when it varies each year t)

• 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 called MACRS)

There are two types of depreciable property

Personal – Income-producing, tangible

property of a corporation, e.g., vehicles, equipment, etc.

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

Note: Land itself is not depreciable

Depreciation Methods

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

Summary of Notation

B – First cost or basis for depreciation n – Recovery period in years SV – Estimated salvage value at end of recovery

period t – year, t = 1, 2, …, n Dt – Depreciation charge for year t Rt – Depreciation rate for year t (R, if same each

year) BVt – Book value after t years of depreciation

Straight Line

Dt =

BVt = B - t×Dt

= BVt-1 - Dt

Rt = R = 1/n

Example: First cost is $50,000

with life of 5 years and estimated salvage of $10,000

Plot SL book value

B = $50,000 S = $10,000 n = 5 years

B – SV n

Straight Line - Example

Year, t Dt BVt

0 $8,000 $50,000

1 8,000 42,000

2 8,000 34,000

3 8,000 26,000

4 8,000 18,000

5 8,000 10,000

SL depreciation: Dt = (50,000-10,000)/5 = $8,000

SL book value: BVt = BVt-1 – Dt

Declining Balance (DB)

•DB write-off of asset value is accelerated compared to SL •Larger annual depreciation amounts in the early years of recovery period •Also called fixed percentage or uniform percentage method •Annual depreciation Dt equals book value at beginning of year BVt-1 (which is same as end of previous year) times fixed rate R

Dt = R× BVt-1

Declining BalanceValues of d are related to SL depreciation rate

2 times SL rate: R = 2/n This is RMAX and is largest allowed by law If n = 5, RMAX = 2/n = 0.4 40% of BV is removed each year Known as double declining balance (DDB)

150% of SL rate: R = 1.5/n

If d is 100% of SL rate, R = 1/n, which is SL depreciation

Notation reminder: R is the fixed percentage of BV removed each year

dt is the depreciation rate for each year t

Declining Balance

Annual depreciation determined in either of 2 ways •Using book value of previous year

Dt = R× BVt-1

•Using first cost basis B

Dt = RB(1-R )t-1

Annual book value determined in either of 2 ways Using first cost basis B

BVt = B(1-R )t

Using sum of accumulated depreciation for years i=1 to t

BVt = B – ΣDi

Declining Balance

Characteristic book value plots of SL, DB and DDB

SL depreciation

DB depreciation at 150% SL rate

DDB depreciation

Declining Balance

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

dt = RB(1-d)t-1

Salvage value is not used in DB method formulas Implied salvage is book value in year n

Implied SV = BVn = B(1-R)n

If a salvage value is estimated, and estimated SV > implied SV, stop depreciating whenever expected SV value is reached

Declining Balance Example

P = $80,000 S = $10,000 n = 5 years Compare BV values for two methods:

DDB and DB at 150% SL rate DB rate is R=1.5/5 = 0.3 DDB rate is RMAX=2/5 = 0.4

cont →

6220.8

Declining Balance Example

•Neither method used the estimated SV of $10,000 to calculate Dt or BVt, except …

•For DDB, depreciation in year 5 is limited, since BV5 would go below S = $10,000 •Only a $368 write-off is allowed in year 5, which is much less than the calculated amount of

D5 = R(BV4) = 0.4(10,368) = $4,147

Note: For the only US-government approved depreciation method, MACRS (covered next), the estimated S is not

used since the entire first cost B is always depreciated to zero

cont →

Declining Balance Example

MACRS

MACRS became the only allowed tax depreciation method in the US in 1986 Statutory depreciation rates dt are tabulated Rates are derived using the DDB or DB method initially with a switch to SL at the optimal time Recovery period n is prescribed and tabulated by asset types MACRS incorporates the half-year convention into the rates and recovery period

MACRS

Personal Property -- Recovery periods are set at 3, 5, 7, 10, 15 and 20 years For n = 3, 5, 7, and 10 -- Depreciation rates start with DDB method, and switch to SL rates to ensure faster write-off of B For n = 15 and 20 -- Depreciation rates start with 150% DB method, and switch to SL rates to ensure faster write-off of B

Half-year convention -- Built in to allow only 50% of first year depreciation; leftover amount is removed in year n+1 (This removes some of the advantage of accelerated depreciation)

MACRS Rates – Personal Property

MACRS Rates – Real Property

oReal property includes buildings and permanent improvements (not land) oMACRS rates utilize SL method for n = 39 years with half-year convention built in oDepreciation rates in % are:

MACRS - Example 1Use MACRS to depreciate asset with

B = $400,000 and n = 3 years

Year,

t

MACRS rate,

dt

Depreciation,

Dt = rate × B

Book value, BVt=BVt-1 - Dt

0 $400,000

1 0.3333 $133,320 266,680

2 0.4445 177,800 88,880

3 0.1481 59,240 29,640

4 0.0741 29,640 0

Totals $400,000

MACRS - ExampleCompare MACRS tax depreciation with DDB book depreciation for B = $400,000 and n = 3 years

MACRS – Example 2 Observations about MACRS and DDB methods

►MACRS always depreciates to $0; no S considered ► MACRS depreciation in year 1 is ½ the DDB or DB amount due to implicit half-year convention ► MACRS takes one additional year for write-off due to implicit half-year convention ► DDB method depreciates to an implied S value at end of the recovery period

►Book value curves vary between the two methods

0

100,000

200,000

300,000

400,000

0 1 2 3 4Year

Book value, $

DDB MACRS

YearDepreciationCalculation

Depreciation Deduction

End-of-YearBook Value

1 $150,000 (0.2) $30,000 $120,000

2 150,000 (0.32) 48,000 72,000

3 150,000 (0.192) 28,800 43,200

4 150,000 (0.1152) 17,280 25,920

5 150,000 (0.1152) 17,280 8,640

6 150,000 (0.0576) 8,640 0

In year 4 there was a $17,280 depreciation deduction.

first cost = $150000

Use MACRS Recovery period is 5 years.

The units-of-production method can be used when the decrease in value of the asset is

mostly a function of use, instead of time. The cost basis is allocated equally over the

number of units produced over the asset’s life. The depreciation per unit of production

is found from the formula below.

Depreciation per unit of production =

$25, $5,

,

000 000

100 000

units

d4 = (10,000 units) ($0.2/unit) = $2,000

BV4= $25,000 - (60,000 units + 10,000 units)($0.20/unit)

= $11,000

= $0.20/unit

TABLE 7-1 The 200% DB Method with Switchover to the SL Method (Example 7-2)

TABLE 7-2 MACRS Class Lives and Recovery Periodsa

TABLE 7-2 (continued) MACRS Class Lives and Recovery Periodsa

TABLE 7-3 GDS Recovery Rates (rk) for the Six Personal

Property Classes

TABLE 7-4 MACRS (GDS) Property

Classes and Primary Methods

for Calculating Depreciation Deductions

Figure 7-1 Flow Diagram for Computing Depreciation

Deductions under MACRS

Figure 7-2 BV Comparisons for Selected Methods of Depreciation in Example 7-7 (Note: The bus is

assumed to be sold in year six for the MACRS-GDS method.)

TABLE 7-5 Corporate Federal Income Tax Rates (2006)

Figure 7-3 The Federal Income Tax Rates for Corporations (Table 7-5) with Incremental Income Tax

for a Proposed Project (assumes, in this case, corporate taxable

income without project > $18,333,333)

Figure 7-4 General Format (Worksheet) for After-Tax Analysis;

Determining the ATCF

TABLE 7-6 ATCF Analysis of Example 7-15

Figure 7-5 Spreadsheet Solution, Example 7-15

TABLE 7-7 ATCF Analysis of Example 7-16 [Reworked Example

7-15 with Machinery in the 10-Year MACRS (GDS) Property Class]

TABLE 7-8 After-Tax Analysis of Example 7-18

Figure 7-6 Summary of Example 7-19

TABLE 7-9 After-Tax Analysis of Purchase Alternative (Example 7-

19)

TABLE 7-10 After-Tax Analysis of Design S1, Example 7-20

TABLE 7-11 After-Tax Analysis of Design S2, Example 7-20

TABLE P7-39 Table for Problem 7-39