Business Mathematics: Depreciation - Units Of Production

Where the use of equipment varies substantially from year to year, the units-of-production method is appropriate for determining the depreciation.

For example, in some years logging operations may be carried on for 200 days, in other years for 230 days, in still other years for only 160 days, depending on weather conditions.

Under this method, depreciation is computed for the appropriate unit of output or production (such as hours, miles, or pounds) by the following formula:

The total number of units used in a year is then multiplied by the unit depreciation to arrive at the depreciation amount for that year. We can express this as

This method has the advantage of relating depreciation cost directly to income.

Example
Cost of a machine, $17,000; salvage, $2,000; estimated life, 8,000 hours.

Over a 5-year lifetime, the machine was in operation for 1,800,1,200, 2,000, 1,400, and 1,600 hours for years 1 to 5, respectively. The computation of the depreciation for those years is


Solved Problems

4.16  An item of machinery, bought on January 5 for $15,000, has an estimated useful life of 30,000 hours and a salvage value of $3,000. In its first year of operation the machine was used for 15,0 hours. What is the depreciation when calculated by the units-of-production method?
 

Solution


4.17  Marion Enterprises bought a photocopier for $5,000. If it was used 3,000 hours the first year, 4,500 hours the second year, and 3,900 hours the third year, find the depreciation for the 3 years, using the units-of-production method. The trade-in value of the copier is $1,000, and its useful life is estimated to be 40,000 hours.
 

Solution


4.18  Steph Pest Control bought a truck costing $11,000 that has an estimated useful life of 100,000 miles and a trade-in value of $2,000. Determine the depreciation if the truck was driven 7,000 miles the first year.
 

Solution


4.19  A used floor polisher was purchased by Liberty Floor Maintenance Company on March 25 for $750. Some repair work amounting to $75 was needed to put the machine into operating condition. Use the units-of-production method to determine the depreciation after 1,000 hours of use. The salvage value of the machine is $25, and its estimated useful life is 5,000 hours.
 

Solution


4.20  Using the units-of-production method, find the depreciation of a machine that produced 3,600 units in its first year of operation. The cost of the machine was $17,000. It has a salvage value of $3,000 and an estimated lifetime output of 50,000 units.
 

Solution


4.21  If Miller & Co. bought a used truck for their lumber business for $6,000 and it cost them $1,500 in repairs before they were able to use it, what is the depreciation according to the units-of-production method at the end of the second year in operation if the truck has a trade-in value of $1,500 and an estimated useful life of an additional 85,000 mi? In the first year, they drove the truck 12,000 mi and in the second year, 14,000 mi.
 

Solution


4.22   Use the units-of-production method to find the depreciation for the following:

Solution


4.23   Using the units-of-production method, find the depreciation of a tractor bought by Misner Farms on April 6 for $23,000. Mr. Misner paid $750 in transportation costs to have the tractor delivered. The tractor has an estimated useful life of 70,000 hours, and its salvage value is $2,750. Misner used the tractor 4,000 hours the first year and 3,950 hours the second year.
 

Solution


4.24   Katz Home Builders started business on October 18. One month prior they purchased a truck for $5,000 and spent an additional $500 to get the truck in operating condition. They also bought a band saw for $500. The truck has an estimated useful life of 50,000 mi and a trade-in value of $1,500. The band saw has an estimated useful life of 5,000 hours and a trade-in value of $50. What is each item’s depreciation at the end of the year if they (a) put 2,085 mi on the truck as of December 31 and (b) used the saw 300 hours?
 

Solution
(a) Truck

(b) Band saw


4.25   Payne Electronics bought an assembler that would assemble 30 transformers per hour. If during the first year of operation 43,200 transformers were assembled, find the depreciation by using the units-of-production method. The assembler cost $150,000 and has a salvage value of $5,000. It is expected to assemble 500,000 transformers during its useful life.
 

Solution


4.26   An item of equipment that has a production capacity of 50 units per hour and an estimated life of 200,000 hours was purchased. The costs involved to get the equipment into operation were $257,500 price, $700 transportation charges, $300 insurance while in transit, and $1,500 installation charge. The trade-in value is $10,000. If it produced 125,000 units in 2,500 hours, what is the depreciation according to the units-of-production method?
 

Solution


4.27   What is the book value of a piece of machinery with an estimated useful life of 750,000 hours and a trade-in value of $6,000, if the machine cost $81,000 and was used for 300,500 hours?
 

Solution


4.28   Find (a) the depreciation and (b) the book value at the end of the third year for an item of equipment that cost $60,000. Delivery of the equipment cost an additional $500, and its estimated useful life is 125,000 mi. The salvage value is $5,500. The equipment was used 22,0 mi the first year, 25,600 mi the second year, and 19,680 mi the third year.
 

Solution
(a)

(b)


4.29   Using the units-of-production method, find the depreciation of a used truck which cost $4,400. Additional costs incurred were $125.89 parts, $258.43 repairs, and $215.68 repainting. The original estimated useful life was 100,000 miles, but the truck had 57,500 miles on it when purchased. Its trade-in value is $750, and the truck was driven 15,899 miles the first year.
 

Solution


4.30   Cook Computer Systems, Inc. purchased a machine that welds components onto printed-circuit boards at a rate of 20 per hour. The machine cost $125,000 plus $2,000 in transportation costs and $3,000 in installation costs. Its estimated useful life is the welding of 100,000 components, and its salvage value is $10,000. Using the units-of-production method, determine the depreciation after 76,550 components have been welded.
 

Solution