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Lecture slides to accompany

Engineering Economy7th edition

Leland Blank

Anthony Tarquin

Chapter 16Depreciation

Methods

© 2012 by McGraw-Hill All Rights Reserved

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LEARNING OUTCOMES

1. Understand basic terms of asset depreciation

2. Apply straight line method of depreciation

3. Apply DB and DDB methods of depreciation

4. Apply MACRS method of depreciation

5. Select asset recovery period for MACRS

6. Explain depletion and apply cost depletion & percentage depletion methods

© 2012 by McGraw-Hill All Rights Reserved

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Depreciation Terminology

Definition: Book method to represent decrease in value of an asset w/time

Two types: book depreciation & tax depreciation

Book depreciation: used for internal accounting to track value of assets

Tax depreciation: used to determine taxes due based on tax laws

In U.S., tax depreciation must be calculated using MACRS;book depreciation can be calculated using any method

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Common Depreciation Terms

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First cost P or unadjusted basis: total installed cost of asset

Book value: remaining undepreciated capital investment

Recovery period: depreciable life of asset in years

Market value: amount realizable if asset were sold in open market

Salvage value: trade-in or market value at end of asset’s useful life

Depreciation rate: fraction of first cost removed by depreciation each year

Personal property: possessions of company used to conduct business

Real property: real estate & all improvements (land not depreciable)

Half-year convention: assumes assets are placed in service in midyear

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Straight Line Depreciation

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Book value decreases linearly with time

Dt = B - Sn

Where: D = annual depreciation charge t = year B = first cost or unadjusted basis S = salvage value n = recovery period

BVt = B - tDt Where: BVt = book value after t years

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Example SL Depreciation

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Solution: (a ) D3 = (P – S)/n = (20,000 – 5000)/5 = $3000

(b) BV3 = B – tDt

= 20,000 – 3(3000) = $11,000

A certain machine has a first cost of $20,000 with a $5,000salvage value after 5 years. Find D and BV for year three.

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Declining Balance Depreciation

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Determined by multiplying BV at beginning of year by fixed percentage, d

Max rate for d is twice straight line rate = 2/nCannot depreciate below book value

Depreciation for year t is given by: Dt = dB(1 – d)t-1 where: Dt = depreciation for year t t = depreciation year d = uniform depreciation rate (2/n for DDB)

B = first cost or unadjusted basis

Book value for year t is given by: BVt = B(1 – d)t

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Example Declining Balance

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(b) BV3 = B(1 – d)t

= 20,000(1 – 0.4)3 = $4320

A certain machine has a first cost of $20,000 with a $4,000salvage value after 5 years. Find (a) the depreciation, and(b) the book value after 3 years using DDB depreciation.

Solution: (a) d = 2/n = 2/5 = 0.4 D3 = dB(1 – d)t-1 = 0.4(20,000)(1 – 0.40)3-1 = $2800

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MACRS Depreciation

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Required method to use in U.S. for tax depreciation

Can depreciate to below salvage value

Dt = dtB Where: Dt = depreciation charge for year t t = year B = first cost or unadjusted basis

BVt = B - ∑Dj Where: BVt = book value after t years Dj = depreciation in year jJ=1

J=t

Get value for dt from table

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Example: MACRS Depreciation

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Solution:

A certain machine has a first cost of $20,000 with a $5,000salvage value after 5 years. Find (a) D and (b) BV for year 3

(a) From table, d3 = 19.20 D3= 20,000(0.1920) = $3,840

(b) BV3 = 20,000 - 20,000(0.20 + 0.32 + 0.192) = $5,760

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MACRS Recovery PeriodRecovery period (i.e. n) is function of property class

Two systems for determining recovery period:

general depreciation system (GDS)

alternative depreciation system(ADS)

IRS publication 946 gives n values for each system. For example: n valueAsset description GDS ADS rangeSpecial manufacturing devices, racehorses, tractors 3 3 - 5 Computers, oil drilling equipment, autos, trucks, buses 5 6 - 9.5Office furniture, railroad car, all property not in other class 7 10 – 15 Nonresidential real property (not land itself) 39 40

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Depletion Methods

Depletion represents decreasing value of natural resources

Two methods: cost depletion and percentage depletion

Cost depletion: Multiply factor by amount of resource removed where factor, CDt = first cost / resource capacity

Percentage depletion: Multiply gross income by PD % from Table

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Example: Depletion A silver mine purchased for $3.5 million is expected to yield one million ounces of silver. Determine the depletion charge in a year when 300,000 ounces are mined and sold for $30 per ounce by (a) Cost depletion, and (b) Percentage depletion.

Solution:(a) Cdt = 3,500,000/ 1,000,000 = $3.50 per ounce Cost depletion = 3.50(300,000) = $1,050,000(b) Percentage depletion = 300,000(30)(0.15) = $1,350,000

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Summary of Important Points

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Two methods of depletion: cost (amount resource removed* CDt factor) & percentage (income*PD % from table)

Two methods for depreciation: tax and book

In U.S., MACRS method is used for tax depreciation

Two systems for determining recovery period: GDS & ADS

Depletion (instead of depreciation) used for natural resources