Engineering Economic Analysis

Unit-oF-Production Depreciation 359

3. Straight-linerate=(B- S)/ N=(10,000 - 5000)/5=$1000

Market value4=$4000

Book value4=10,000 - (4)(1000)=$6000

Loss=6000 - 4000=$2000

If the asset were disposed ofduring the year rather than at year's end,then the straight-

line depreciation deduction would have to be prorated for the number of months during

the year that the asset was in service. There is no half-year convention with the historical

depreciation methods. For example, if disposal occurred on September 30 of Year 4,

d4=(9/12)(1000) =$750.

(Note: In Case 1 it was shown that the required half-year convention did not affect the total

deductions from taxable income. This is true for the other cases as well, since both recaptured

depreciation and losses are treated as ordinary income.)

UNIT-Of-PRODUCTION DEPRECIATION

At times the recovery of depreciation on a particular asset is more closely related to use

than to time. In these few situations (and they are rare), the unit-of-production (UOP)

depreciation in any year is

... Production for year

UOP deprecIatIOn III any year = ... (B- S) (11-6)

Total lIfetime production for asset

This method might be useful for machinery that processes natural resources if the

resources will be exhausted before the machinery wears out. Historically,this method was

sometimes used for construction equipment that had very heavy use in some years and very

light use in others. It is not considered an acceptablemethod for general use in depreciating

industrial equipment.

For numerical sjrnilarity with previous examples, assume that equipment costing $900 has been

purchased for use in a sand and gravel pit. The pit will operate for 5 years, while a nearby airport

is being reconstructed and paved. Then the pit will be shut down, and the equipment removed

and sold for $70. Compute the unit-of-production (UOP) depreciation schedule if the airport

reconstruction schedule calls for 40,000 m3 of sand and gravel as follows.:

Year Required Sand and Gravel (m3)

1 4,000

2 8,000

3 16,000

4 8,000

5 4,000

:

::I =

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