# Section 3 Dr.Hoda’s part Depreciation

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Section 3 Dr.Hoda’s part Depreciation
Economics Section 3 Dr.Hoda’s part Depreciation Eng. Reda Zein

Depreciation A noncash expense that reduces the value of an asset as a result of wear and tear, age, or obsolescence. Most assets lose their value over time (in other words, they depreciate), and must be replaced once the end of their useful life is reached. There are several accounting method that are used in order to calculate an assets depreciation costs over the period of its useful life.. -It represents the largest single item of FCI - Used in estimating the capital investment

Depreciation methods 1- Straight line method: 𝑑= 𝑉 𝑜 − 𝑉 𝑠 𝑛 Where: d: depreciation charge, Vo: orignal value, Vs: salvage value, n: service life ( 𝑉 𝑜 − 𝑉 𝑠 ): is the total depreciated value. 2- Use or production method: 𝑑= 𝑚𝑖𝑙𝑎𝑔𝑒 (𝑢𝑠𝑒) 𝑖𝑛 𝑡ℎ𝑒 𝑦𝑒𝑎𝑟 𝑡𝑜𝑡𝑎𝑙 𝑚𝑖𝑙𝑎𝑔𝑒 ∗( 𝑉 𝑜 − 𝑉 𝑠 )≠const

Depreciation methods 3- Double declining balance method: 𝑑=2∗ 1 n ∗remaining cost 4- Sum of years digits method: 𝑑= Useful service life remaining 𝑖=1 𝑛 𝑖 ∗( 𝑉 𝑜 − 𝑉 𝑠 ) Where: n: Total service life, Useful life remaining= years remaining of service life at the beginning of year considered 𝑖=1 𝑛 𝑖 : Arithmetic sum of digits of years 5) Thinking vund method (will not be needed in sheet) Depends on interest yearly on money (if Iput dep. Money in a bank)

Let’s begin our sheet

2) A reactor of special design is the major item of equipment in a small chemical plant. The initial cost of the completely installed reactor is \$60,000 and salvage value at the end of the useful life is estimated to be \$10,000. Excluding depreciation costs for the reactor, the total annual expenses for the plant are \$100,000. How many years of useful life should be estimated for the reactor if 12% of the total annual expenses for the plant are due to the cost of reactor depreciation? The straight line method for determining depreciation should be used. (Ans.=3.7 year)

3) Apiece of equipment originally costing \$40,000 was put into use 12years ago. At the time the equipment was put into use, the service life was estimated to be 20 years and the salvage and the scrap value at the end of the service life were assumed to be zero. On this basis, straight line depreciation fund was set up. The equipment can now be sold for \$10,000 and a more advanced model can be installed for \$55,000. Assuming the depreciation fund is available for use, how much new capital must be supplied to make the purchase? (Ans. =\$21,000)

4) A piece of equipment having a negligible salvage value is estimated to have a service life of 10 years. The original cost of equipment was \$40,000. Determine the following: a- The depreciation charge during the 5th year if straight line depreciation is used. b- The depreciation charge during the 5th year if sum–of-years- digits depreciation is used. c- The percent of original investment paid off in the first half of the service life using sum–of-years- digits method. d- The percent of original investment paid off in the first half of the service life using the double declining balance method. (Ans.:a-\$4,000, b- \$4363.6, c-72.7%, d- 67.2%)

5) The original investment for an asset was \$10,000 and the asset was assumed to have a service life of 12 years with \$2,000 salvage value at the end of service life. After the asset has been in use for 5 years, the remaining service life and final salvage value are re-estimated at 10 years and \$1,000 , respectively. Under these conditions, what is the depreciation cost during the sixth year of the total life if straight line depreciation is used ? (Ans.:\$566.7)

7) In order to make it worth while to purchase a new piece of equipment, the annual depreciation costs for the equipment cannot exceed \$3,000 at any time. The original cost of equipment is \$30,000 and it has zero salvage and scrap value. Determine the length of service life necessary if the equipment is depreciated by (a) The straight-line method and (b) The sum–of-years- digits method. (Ans.: (a) 10 years (b) 19 year )

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