Business Mathematics: Depreciation - Straight-Line Method

This is the simplest and most widely used depreciation method. Under this method an equal portion of the cost (above salvage value) of the asset is allocated to each period of use.

The periodic depreciation charge is expressed as


Example 1
If the cost of a machine is $17,000, its salvage value $2,000, and its estimated useful life 5 yr, the straight-line depreciation is

The date on which a piece of equipment is bought has an effect on the amount of depreciation taken for the first year. Similarly, if the equipment is later sold, the sale date determines the amount of depreciation taken in the year of sale.

Example 2
Suppose that the machine in Example 1 was bought on March 26. Since this date is closer to April 1 than March 1, the depreciation for the first year (ending December 31) is based on April 1 acquisition.
From the yearly depreciation of $3,000 (Example 1), we determine the monthly depreciation as follows:
$3,000/yr ÷ 12 mo/yr = $250/mo depreciation
Since April 1 through December 31 encompasses 9 months, we multiply the monthly depreciation by 9 to find the depreciation applicable to the first year.
$250/mo × 9 mo = $2,250 depreciation for 1st year
For the second through the fifth years, the full $3,000 per year depreciation is taken, unless the machine is sold. If the machine is sold before the end of a given year, the amount of depreciation applied in that year is calculated on the fraction of the year during which the machine was used, as above.
At any point in time, the book value is the cost of the equipment less any depreciation to date.

Example 3
If bought on March 26 (Example 2), the end of the first year (December 31) book value of the machine in Example 1 is

At the end of the fifth year, the book value of this machine is its salvage value, $2,000.

Solved Problems

4.1 On January 1 Greenwood Industries purchased machinery for $5,000. It is estimated that the machinery will have a useful life of 5 years and a salvage value of $500. Using the straight-line method, determine the depreciation per year.
 

Solution


4.2 Find the amount of depreciation per year if a fixed asset bought on January 1 for $15,000 has an estimated life of 10 years and a salvage value of $3,000.
 

Solution


4.3 If Miller Farms purchased equipment on January 5 for $35,000, calculate the depreciation per year using the straight-line method. The salvage value is $7,000, and the estimated useful life is 10 years.
 

Solution


4.4 Harold Enterprises bought office furniture on May 12. The purchase price was $4,000 and the estimated useful life is 5 years. The salvage value is $550. Find the depreciation as of December 31 (same year).
 

Solution


4.5 A delivery truck was purchased by Wade Florists on September 12. The initial cost of the truck was $9,000, but some new parts were needed, totaling $800. Under the straight-line method, what is the depreciation to the nearest cent at the end of the year if the estimated useful life of the truck is 5 years and the salvage value is $1,200?
 

Solution

First-year depreciation:
$1,720 ÷ 12 mo = $143.33/mo
$143.33 × 4 mo = $573.32 depreciation at end of yr

4.6 What is the amount of depreciation at the end of the second year, if a piece of equipment was purchased on July 24 for $1,300, its estimated useful life is 8 years, and trade-in value is $100?
 

Solution


4.7 A dishwasher was purchased by the Check-Inn Restaurant on October 1. The purchase price was $1,200 and the installation cost was $300. The estimate useful life of the dishwasher is 6 years and its salvage value is $300. What is the amount of depreciation to the nearest cent at the end of the fourth year?
 

Solution


4.8 If office furniture purchased on January 2 for $8,100 has an estimated useful life of 6 years and a trade-in value of $750, what is the book value at the end of the fifth year?
 

Solution

End of fifth-year depreciation:
$1,225 × 5 yr = $6,125 depreciation for 5 yr
Book value at end of fifth year:


4.9  Lorino Plumbing and Heating purchased tools on February 18 for $800. The salvage value of the tools is $200, and the estimated life is 10 years. What is the book value at the end of the fourth year?
 

Solution

End of fourth-year depreciation:
$60 ÷ 12 mo = $5/mo
$5 × 10 mo = $50 depreciation for 1st year
$60 × 3 yr = $180 depreciation for years 2, 3, and 4
$180 + $50 = $230 depreciation at end of 4th yr

Book value at end of fourth year:
Cost — depreciation = book value
$800 - $230 =
$570 =

4.10   Determine the depreciation rate per year for an estimated useful life of (a) 10 yr, (b) 50 yr, (c) 8yr, (d) 5 yr, (e) 16 yr, and (/) 20 yr.
 

Solution


4.11   Determine the (a) depreciation rate, (b) yearly depreciation, and (c) book value after 10 years of a building that cost $100,000 on January 7. After its estimated useful life of 25 yr, the salvage value is $20,000.
 

Solution

(b) We can rewrite the formula from Sec. 4.2 in terms of depreciation rate, as follows:

(c) Book value after 10 yr:


4.12   Find the annual depreciation for the following:

Solution


4.13   Prepare a depreciation schedule for a piece of machinery purchased January 10 for $7,700. Transportation costs amounted to $300. The estimated useful life is 10 years, and the machine has a salvage value of $800. The depreciation schedule spans the estimated life of the machine and includes the depreciation rate for each year, the dollar amount of that year’s depreciation, the book value, and each year’s accumulated depreciation.
 

Solution



4.14   Marshall Painters bought 15 paint sprayers at a cost of $80 each. The delivery charge for all 15 sprayers was $80, and delivery was on August 16. Each sprayer has an estimated useful life of 8 years and no salvage value. What is the depreciation on December 31 of the sixth year?
 

Solution
Cost:

Depreciation at end of sixth year:
$160/yr ÷ 12 mo/yr = $13.33/mo
$13.33 × 4 mo = $53.32 depreciation for 1st yr
$160 × 5 yr = $800 depreciation for years 2-6
$800 + $53.32 = $853.32 depreciation Dec. 31 of 6th yr

4.15   What is the book value at the end of the third year for each of the following:

 

Solution