Business Math

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Business Math

Chapter 16: Depreciation

2Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

16.1 Depreciation methods for financial statement reporting

Depreciate an asset and prepare a depreciation schedule

using the straight-line method

using the units-of-production method

using the sum of the years’ – digits method

Using the declining balance method


Key Terms

Assets: properties owned by the business, including anything of monetary value and anything that can be exchanged for cash or other property.

Estimated life or useful life: the number of years an asset is expected to be useable.

Salvage value, scrap value, or residual value: an estimated dollar value of an asset at the end of the asset’s estimated life.


Depreciation: the amount an asset decreases in value from its original cost.

Straight-line depreciation: a method of depreciation in which the amount of depreciation of an asset is spread equally over the number of years of useful life of the asset.

Total cost: the cost of an asset including shipping and installation charges.

Depreciable value: the cost of an asset minus the salvage value.

Key Terms


16.1.1. Use the straight line depreciation method

Find the total cost of the assetTC = cost + shipping + installation

Find the depreciable valueDepreciable value = TC – salvage value

Find the yearly depreciation:= depreciable value ÷ years of expected life


Look at this example Use the straight-line method to find the yearly

depreciation for a plating machine that has an expected useful life of 5 years. The plating machine cost $27,300; its shipping costs totaled $250, installation charges came to $450 and its salvage value is $1,000.

TC= $27,300 + $250 + $450 = $28,000

Depreciable value = $28,000 - $1,000 = $27,000

Yearly depreciation = $27,000 ÷ 5 = $5,400


Try this example

A labeling machine cost $43,000. Installation costs totaled $1,250 and shipping costs totaled $2,250. It has an expected useful life of 10 years. Its salvage value is $2,000. Use the straight-line method of depreciation to find the yearly depreciation for the labeling machine.

The depreciation is $4,450 per year.


Depreciation schedule: a table showing the year’s depreciation, the accumulated depreciation, and the end-of-year book value.

Accumulated depreciation: the current year’s depreciation plus all previous years’ depreciation.

End-of-year book value: total cost minus depreciation for the first year. Thereafter, it is the previous year’s end-of-year book value minus the current year’s depreciation.

Key Terms


16.1.2 Use the units-of-production method

Takes into account an asset’s use in terms of production, for example: Items produced Miles driven Hours operated Number of times it has performed a specific operation

Companies that use this method internally often adjust to a method acceptable by the

IRS for tax-reporting purposes.


Find the unit depreciation

Unit depreciation =

Depreciable valueUnits produced during expected life

Depreciation for units produced = unit depreciation x units produced


Look at this example

A label making machine that costs $28,000 after shipping and installation is expected to print 50,000,000 labels during its useful life. If the salvage value of the machine is $1,000, find the unit depreciation and the depreciation for printing 2,125,000 labels.

(go to next slide)


Find the depreciation Unit depreciation = depreciable value ÷ units

produced during expected life

Unit production = $27,000/ 50,000,000

Unit depreciation = $0.00054

Depreciation for 2,125,000 labels = $0.00054 x 2,125,000 = $1,147.50

The depreciation for that number of labels is $1,147.50.


Try this example

A small pickup truck was purchased for occasional deliveries during the busy season of Eager Enterprises. Total cost of the truck was $24,000. The salvage value is $2,500. The expected number of miles to be driven over the truck’s useful life is 100,000. Find the depreciation after one year is the truck has been driven 3,000 miles.

$645 is the depreciation amount


16.1.3 Use the sum-of-the years’ digits method

Sum-of-the-years’ digit method: A depreciation method which allow the greatest depreciation the first year and decreasing amount each year thereafter.

Year’s depreciation rate: the depreciation rate for any given year of a depreciation schedule.


Find the year’s depreciation

The numerator of the year’s depreciation rate is the number of years of expected life remaining.

The denominator of the year’s depreciation rate is the sum of the numbers from 1 to the years of expected life.

Shortcut for finding the sum:n(n+1) = sum 2


Look at this example Find the depreciation for each of the five years

of expected life of a bottle capping machine that costs $27,300 and has a shipping cost of $250 and an installation cost of $450, and a salvage value of $1,000. Make a depreciation schedule.

Denominator = 5 (6) ÷ 2 = 15

Numerator for year 1 = 5; year 2 = 4 and so on.

Depreciable value = TC – salvage value

Depreciable value = $27,000


Depreciation schedule Year 1 = $27,000 x 5/15 = $9,000

End of year book value = $28,000-$9,000=$19,000

Year 2 = $27,000 x 4/15 = $7,200End of year book value = TC – accumulated depreciation = $11,800

Now, calculate the depreciation and book value for Years 3, 4, 5.

Y 3 $5,400 and end-of year book value is $6,400. Y 4 $3,600 and end-of year book value is $2,800. Y 5 $1,800 and end-of year book value is $1,000.


16.1.4 Use the declining balance method of depreciation

A depreciation method that provides for large depreciation in the early years of the life of an asset.

Double-declining rate (or 200% declining-balance method): a declining balance depreciation that is twice the straight-line depreciation.

150% declining rate: a common declining balance rate that is 1 ½ times the straight line rate.


Find the depreciation Yearly double declining rate = yearly straight

line depreciation rate x 2

Yearly 150% declining depreciation rate = yearly straight line depreciation rate x 1.5

First year’s depreciation = total cost x yearly depreciation rate

For all other years: Year’s depreciation = previous end-of-year book value x yearly depreciation rate.


Look at this example An ice-cream freezer has a useful life of six

years. Find the yearly:

straight line rate expressed as a decimal and a percent

Double-declining rate expressed as a decimal and a percent.

150%-declining rate expressed as a decimal and a percent.


The rates

Straight-line = 1/6 or .1667 or 16.67%

Double-declining = 2(1/6) = 1/3 or 33%

150% declining rate = 1.5 (1/6) = 0.25 or 25%


Tip! In declining-balance depreciation, the

depreciation for the first year is based on the total cost of the asset.

Do not subtract the salvage value from the total cost to find the depreciation in the first year.

The end-of-year book value for any year cannot drop below the salvage value of the asset. If the depreciation would cause it to drop below the salvage value, the year’s ending value will be the salvage value.


Look at this example A packaging machine costing $28,000 with an

expected life of five years and a resale value of $1,000 is depreciated by the declining balance method at twice the straight-line rate. Prepare a depreciation schedule.

Year one (2) 1/5 = 2/5 or 40% or .40 $28,000 x 40% = $11,200 End of year 1 book value = TC – depreciation End of year 1 = $28,000- $11,200 = $16,800


Finish the depreciation schedule

Year Two = previous end-of-year book value x double-declining rate$16,800 x 0.4 = $6,720

End-of-year Two book value = previous end-of-year book value – depreciation = $16,800 - $6,720 = $10,080

(go to next slide)


Years 3, 4 and 5 Year Three =

previous end-of-year book value x double-declining rate = $10,080 x 0.4 = $4,032

End-of- year Three book value = $10,080 - $4,032 = $6,048

Year Four depreciation = $2,419.20End of year Four book value = $3,628.80

Year Five depreciation = $1,451.52End-of-year Five book value = $2,177.28


16.2 Depreciation Methods for IRS reporting

Depreciate an asset and prepare a depreciation schedule using the modified accelerated cost-recovery system (MACRS)

Depreciate an asset after taking a section 179


16.2.1 Using MACRS

In, 1981, the IRS enacted an accelerated cost-recovery system (ACRS) for the depreciation of property put into service after that date.

Allowed businesses to write off cost of assets more quickly.

Objective was to encourage businesses to invest in more assets despite an economic slowdown at the time.


Table 16-5

Table 16-5 indicates that each recovery period has a depreciation rate for one year more than the recovery period indicates.

First and last year in the recovery period are partial years.

Greatest amount of depreciation is realized in the second year, which is the first full year.


Using the MACRS Method

Using the IRS publication, determine the asset’s recovery period and find the appropriate table.

Find the MACRS rate using Table 16-5

Multiply the year’s MACRS rate by the total cost of the asset.

Year’s Depreciation = Year’s MACRS rate x total cost


Why is this easier than traditional depreciation methods?

1. You do not have to find a depreciable value.

2. You do not have to determine a salvage value.

3. The useful life is determined by the property classes.


Look at this exampleFind the depreciation for each year for a boiler that was purchased for $28,000 and placed in service at midyear under the MACRS method of depreciation as a five-year property.

Year 1 depreciation = MACRS rate x Total Cost Year 1 depreciation = 20% x $28,000 Year 1 depreciation = $5,600 Do the subsequent years through Year 6. Check calculations on the following slide.


Check your calculations.

Year 2 depreciation = $8,960

Year 3 depreciation = $5,376

Year 4 depreciation = $3,225.60



The sum of yearly depreciations equals the total cost of the asset ($28,000).


16.2.2 Depreciate an asset after taking a section 179 deduction

For tax purposes, it can be treated as a one-time expense, rather than as a capital expenditure that is depreciated over several years.

The amount that is claimed under Section 179 is subtracted from the original price of the property and the balance can be depreciated using any of the approved methods of depreciation.

Eligible only in the first year that a qualifying property is purchased and placed into service.


Section 179 Deduction Property must be placed in service for business

purposes only. A property put in service first for personal use and subsequently for business use would not be eligible.

Eligible property, in general, is tangible, depreciable personal property that is used for the production of income.

Can only be used to reduce taxable income, not to create a net loss; estates and trusts cannot claim the Section 179 deduction.


How to depreciate an asset after taking a Section 179 deduction

Decide how much of the maximum section 179 allowance to apply to the asset.

Subtract the elected section 179 deduction from the total cost of the asset.

Apply an approved depreciation method to the value from the previous step, instead of the actual total cost.


Look at this example

Find the first year depreciation using MACRS for the 7th Inning’s kitchen, that is purchased and placed into service at midyear. The price of the property is $125,250 and the maximum $100,000 section 179 deduction is elected.

$125,250-$100,000 = $25,250

$25,250 x 14.29% (MACRS rate) = $3,608.23

The first year’s depreciation is $3,608.2336

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