Business Mathematics: Depreciation Methods Compared

The four principal methods of depreciation are compared in this table below.

Over a 5-year lifetime, the asset was in operation for 1,800, 1,200, 2,000,1,400, and 1,600 hours per year, respectively. The cost of the asset was $17,000, and the scrap value is $2,000.

Table: Annual Depreciation Charge


Solved Problems

4.61   A fixed asset costing $60,000 and having an estimated salvage value of $5,000 has a life expectancy of 10 years. Compare the results of the various depreciation methods by filling in the tables below. Take twice the straight-line rate as the rate in the double declining balance method.

Straight-Line Method


Sum-of-the-Years‘-Digits Method


Double Declining Balance Method

 

Solution:

Straight-Line Method


Sum-of-the-Years'-Digits Method


Double Declining Balance Method

More Problems:

4.62 Using the straight-line method of depreciation, find the amount of depreciation per year if a fixed asset bought on January 6 for $17,000 has an estimated life of 15 years and a salvage value of $2,000.

4.63 Muller Printers bought printing equipment on July 6. The purchase price was $3,700, and the estimated useful life is 4 years. The salvage value is $700. Find the depreciation as of December 31 (same year) by using the straight-line method.

4.64 Using the straight-line method, calculate the amount of depreciation at the end of the second year on a piece of machinery purchased on October 28 for $4,650. The estimated useful life is 5 years and the trade-in value is $1,650.

4.65 A computer was purchased by Hill Enterprises on February 1. The purchase price was $2,000, and installation cost was $720. The estimated useful life is 10 years, and the salvage value is $500. What is the amount of straight-line depreciation (to the nearest cent) at the end of the third year?

4.66 If a photocopier purchased on January 3 for $13,400 has an estimated useful life of 15 years and a trade-in value of $950, what is the book value at the end of the sixth year according to the straight-line method of depreciation?

4.67 Determine the depreciation rate per year for the following estimated useful lives: 4 years, 25 years, and 32 years.

4.68 Prepare a depreciation schedule for a piece of equipment purchased on January 8 for $5,000. Transportation costs amounted to $500. The estimated useful life is 4 years, and the salvage value is $500. Use the straight-line method of depreciation.

4.69 Using the straight-line method of depreciation, determine the book value at the end of the fourth year for the following:


4.70 An item of equipment was bought on January 1 for $30,000. It has an estimated useful life of 100,000 hours and a salvage value of $4,000. If it was used for 35,650 hours in its first year of operation, what is the depreciation according to the units-of-production method?

4.71 A used dishwasher was purchased by Faine Restaurant on April 3 for $1,500. Repair work totaling $300 was needed before putting the machine into operation. Using the units-of-production method, determine the depreciation after 5,760 hours of use if the salvage value is $50 and the estimated useful life is 57,750 hours.

4.72 Using the units-of-production method, find the depreciation on a piece of assembly-line equipment that produced 9,750 units during its first year in operation. The cost of the equipment was $40,000. It has a salvage value of $2,500 and an estimated lifetime output of 75,000 units.

4.73 K&M Painting Contractors started business on June 1. One month prior they purchased a van for $8,000 and incurred additional costs amounting to $1,000 to get the van in operating condition. They also bought a paint sprayer for $300. The van has an estimated useful life of 100,000 mi and a trade-in value of $2,000. The paint sprayer has an estimated useful life of 2,750 hours and a trade-in value of $25. What is the depreciation, based on the units-of-production method, at the end of the year if they put 5,670 mi on the van as of December 31 and used the paint sprayer 250 hours?

4.74 Roe Computers bought an assembler that assembles 50 circuit parts per hour. If during the first year of operation the machine assembled 68,430 circuits, find the depreciation by using the units-of-production method. The assembler cost $230,000, has a salvage value of $10,000, and is expected to assemble 1 million circuits during its useful life.

4.75 What is the book value of a piece of equipment that cost $70,000, was used 237,000 hours, and has an estimated useful life of 500,000 hours and a trade-in value of $5,000?

4.76 Using the units-of-production method, find the depreciation of a used truck that cost $3,700. Additional costs incurred were $335.69 parts, $312.97 repairs, and $151.34 repainting. The original estimated useful life was 150,000 mi, but the truck had 87,965 miles on it when purchased. The trade-in value is $500, and the truck was driven 9,623 mi during the year.

4.77 Office furniture was purchased by Chester Company on January 1 for $2,000. Its estimated useful life is 20 years, and it has a salvage value of $250. Using the double declining balance method of depreciation, what is the depreciation at the end of the first year?

4.78 Equipment was bought on January 10 for $30,000. It has an estimated useful life of 25 years and a trade-in value of $3,000. Determine the book value at the end of the first year by using the double declining balance method of depreciation.

4.79 Determine the accumulated depreciation at the end of the second year by using the double declining balance method of depreciation on a tractor that cost $9,000. Its estimated useful life is 10 years, and the trade-in value is $500. It was bought on October 20.

4.80 If equipment that cost $100,000 and has a trade-in value of $10,000 was put into use on January 3, what is the book value at the end of the second year if said equipment has an estimated useful life of 50 years and the double declining balance method of depreciation is used?

4.81 For the following, find the book value to the nearest dollar at the end of the first year by using the double declining balance method of depreciation:
 

4.82 A conveyor with an estimated useful life of 8 years and a salvage value of $400 was purchased for $5,000. Determine the book value at the end of the second year by using the double declining balance method of depreciation.

4.83 Mullen Corporation purchased a computer on December 31 for $7,000. Its estimated useful life is 20 years, and the salvage value is $1,000. Find the book value at the end of the first year by using the double declining balance method of depreciation.

4.84 According to the double declining balance method, what is the accumulated depreciation at the end of 2 years on a piece of machinery bought on January 13 for $4,000? The estimated useful life is 5 years, and the salvage value is $200. (Round the depreciation to the nearest dollar.)

4.85 Find the sum of the years for the following life expectancies: 4 years, 3 years, and 20 years.

4.86 Determine the first year’s depreciation fraction in the sum-of-the-years’-digits method of depreciation for the following estimated useful lives: 15 years, 5 years, and 8 years.

4.87 Using the sum-of-the-years’-digits method, find the first year’s depreciation on a tractor that cost the town of Hill $10,000 and has an estimated useful life of 20 years and a salvage value of $1,000.

4.88 Billy purchased three trucks costing $10,000 each for his painting business. The trucks have a trade-in value of $1,000 each and an estimated life of 15 years each. What is the depreciation on all three at the end of the first year if purchase was made on January 10? (Round the depreciation to the nearest dollar.)

4.89 Use the sum-of-the-years’-digits method to find the book value (to the nearest cent) at the end of the first year on a piece of machinery that cost $15,425. It has a salvage value of $2,425 and an estimated useful life of 10 years.

4.90 Using the sum-of-the-years’-digits method, determine the accumulated depreciation at the end of 2 years on an item that cost $90,000 and has an estimated useful life of 50 years and a salvage value of $5,000. (Round the depreciation to the nearest dollar.)

4.91 Use the sum-of-the-years’-digits method to find the depreciation at the end of the first year for the following:

Answers to Above Problems:

4.62 $1,000
4.63 $375
4.64 $700
4.65 $647.50
4.66 $8,420
4.67 25%, 4%, 3^%
4.69 (a) $7,600, (b) $4,000, (c) $28,i
4.70 $9,269
4.71 $172.80
4.72 $4,875
4.73 $396.90 van, $25 paint sprayer
4.74 $15,054.60
4.75 $39,190
4.76 $620.49
4.77 $200
4.78 $27,600
4.79 $2,040
4.80 $92,160
4.81 $2,400, $25,560
4.82 $2,812.50
4.83 $6,300
4.84 $2,560
4.85 10, 6, 210
4.86 15/120, 5/15, 8/36
4.87 $857.14
4.88 $3,375
4.89 $13,061.36
4.90 $6,600
4.91 (a) $2,041.56, (b) $628.57