Chapter 7: Depreciation Lecture 13 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).

or natural resource (by depletion) Depreciation Methods TOPICS Depreciation terminology Straight line Declining balance MACRS units-of-production PURPOSE Use a specific model to reduce the value of an Asset (by depreciation) or natural resource (by depletion)

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 First cost, B – Total cost of asset including purchase, installation, fees, etc. Salvage, SV – Estimated market value at end of recovery period BV, $ Book Value, BV – Remaining, undepreciated investment after all depreciation to date is removed SV Time, years Recovery period, n – Depreciable life in years. Tax and book depreciation lives often vary

Terminology Some 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

Some methods used in the US and other countries 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 B – SV 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

Straight Line - Example SL depreciation: Dt = (50,000-10,000)/5 = $8,000 SL book value: BVt = BVt-1 – Dt Year, t Dt BVt $8,000 $50,000 1 8,000 42,000 2 34,000 3 26,000 4 18,000 5 10,000

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

Values of d are related to SL depreciation rate Declining Balance Values 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 Dt = R× BVt-1 Dt = RB(1-R )t-1 BVt = B(1-R )t 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 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

Implied SV = BVn = B(1-R)n 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 cont → 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

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

Use MACRS to depreciate asset with MACRS - Example 1 Use 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 $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 Totals

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

Observations about MACRS and DDB methods 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 DDB MACRS

Use MACRS Recovery period is 5 years. first cost = $150000 Use MACRS Recovery period is 5 years. In year 4 there was a $17,280 depreciation deduction. Year Depreciation Calculation Deduction End-of-Year Book 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 8,640 6 150,000 (0.0576)

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 = 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 32

TABLE 7-2 (continued) MACRS Class Lives and Recovery Periodsa 33

TABLE 7-3 GDS Recovery Rates (rk) for the Six Personal Property Classes 34

TABLE 7-4 MACRS (GDS) Property Classes and Primary Methods for Calculating Depreciation Deductions 35

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) 38

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 41

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] 43

TABLE 7-8 After-Tax Analysis of Example 7-18 44

Figure 7-6 Summary of Example 7-19

TABLE 7-9 After-Tax Analysis of Purchase Alternative (Example 7-19) 46

TABLE 7-10 After-Tax Analysis of Design S1, Example 7-20 47

TABLE 7-11 After-Tax Analysis of Design S2, Example 7-20 48

TABLE P7-39 Table for Problem 7-39 49