UNIVERSITY OF SCIENCE AND TECHNOLOGY OF SOUTHERN PHILIPPINES Alubijid | Cagayan de Oro | Claveria | Jasaan | Oroquieta | Panaon Depreciation Methods Subject: Engineering Economy Instructor: Engr. Ma. Leona Maye B. Pepito MLMPepito EnggEcon v.1 1 What is Depreciation ? - a reduction in the value of an asset with the passage of time, due in particular to wear and tear. -is an accounting method of allocating the cost of a tangible or physical asset over its useful life or life expectancy. -it represents how much of an asset's value has been used up. MLMPepito EnggEcon v.1 2 Depreciation Terms Fixed Asset - the asset which bought for a long run, which is bought by a business for its operational use e.g. Building, Machinery, Lant Et.c Book Value (BV) - the asset's first cost minus the asset's accumulated depreciation. Original Value or First Cost (FC)- is related to the original value or we can say buying value of the fixed Asset. Rate of Depreciation (ROD) - it is a fixed rate of depreciation which we have reduced every financial or calendar year from the original value of the fixed Asset. Scrap Value (SV) - is the value of an asset when it is no longer usable. Scrap value is also referred to as Salvage Value or Residual Value. MLMPepito EnggEcon v.1 3 Methods of Depreciation 1. 2. 3. 4. 5. 6. 7. 8. Straight Line Method Sinking Fund Method Sum of the Years Digit Method Declining Balance Method Double Declining Balance Method Working Hours Method Constant Unit Method Output Method MLMPepito EnggEcon v.1 4 1. Straight Line Method In straight-line depreciation, the expense amount is the same every year over the useful life of the asset. Depreciation Formula for the Straight Line Method: Annual Depreciati on, A D = (First Cost – Scrap Value) / Useful life = (FC - SV) / n Total Depreciation after “x” years, DT = (FC - SV) ( x) n Book Value , BV = FC - D T MLMPepito EnggEcon v.1 5 1. Straight Line Method MLMPepito EnggEcon v.1 6 1. Straight Line Method Example: Consider a piece of equipment that costs Php 25,000 with an estimated useful life of 8 years and a no salvage value. How much is the depreciation expense per year for this equipment using straight line method. Solution: Annual Depreciation, AD = (FC – SV) / n Annual Depreciation, AD = (Php25,000 – 0) / 8yrs Annual Depreciation, AD = Php 3,125 / yr MLMPepito EnggEcon v.1 7 Methods of Depreciation 1. 2. 3. 4. 5. 6. 7. 8. Straight Line Method Sinking Fund Method Sum of the Years Digit Method Declining Balance Method Double Declining Balance Method Working Hours Method Constant Unit Method Output Method MLMPepito EnggEcon v.1 8 2. Sinking Fund Method Sinking Fund Method is a depreciation method wherein funds will accumulate for replacement purposes. The formulas for Sinking Fund Method of Depreciation are: Annual Depreciation, A D = (FC - SV) (i ) (1 i) n 1 A (1 i) x 1 Total Depreciati on after “x” years , D T = i Book Value, BV = FC - D T MLMPepito EnggEcon v.1 9 2. Sinking Fund Method Example: A machine costs Php 300,000 with a salvage value of Php 50,000 at the end of its life of 10 years. If money is worth 6% annually, use Sinking Fund Method and determine the depreciation at the 6th year. Solution a. Solve for the annual depreciation. (FC - SV) (i) Annual Depreciation, A D = (1 i) n 1 (300,000 - 50,000) (0.06) AD = (1 0.06)10 1 A D = Php 18,967 MLMPepito EnggEcon v.1 10 2. Sinking Fund Method b. Solve for the depreciation in the 6th year. Total depreciation after x years, DT A (1 i)x 1 DT = i (18967)(1 0.06)6 1 DT = 0.06 DT = Php132,300.86 MLMPepito EnggEcon v.1 11 Methods of Depreciation 1. 2. 3. 4. 5. 6. 7. 8. Straight Line Method Sinking Fund Method Sum of the Years Digit Method Declining Balance Method Double Declining Balance Method Working Hours Method Constant Unit Method Output Method MLMPepito EnggEcon v.1 12 3. Sum of the Years Digit Method Sum of the Years Digit Method (SOYD) is an accelerated depreciation technique based on the assumption that tangible properties are usually productive when they are new, and their use decreases as they become old. The formulas for the SOYD Method of Depreciation are: Sum of years = (n / 2) (n + 1) Annual depreciation at 1st year= (FC - SV) (n / Sum of years) Annual depreciation at 2nd year = (FC -SV) ((n-1) / Sum of years) Book Value = FC - Total depreciation at the end of nth year MLMPepito EnggEcon v.1 13 3. Sum of the Years Digit Method Example: An equipment costs Php 1,500,000. At the end of its economic life of five years, its salvage value is Php 500,000. Using Sum of the Years Digit Method of Depreciation, what will be its book value for the third year? Solution: a. Solve for the sum of years. Sum of years = (n / 2) (n + 1) Sum of years = (5 / 2) (5 + 1) Sum of years = 15 years b. Solve for the total depreciation up to the third year. Total depreciation = (FC - SV) (5 + 4 + 3) /15 Total depreciation = (1,500,000 - 500,000) (12) / 15 Total depreciation = Php 800,000 MLMPepito EnggEcon v.1 14 c. Solve for the book value in the third year. Book Value = FC - Total depreciation Book Value = 1,500,000 - 800,000 Book Value = Php 700,000 Therefore, the book value for the third year is Php 700,000. MLMPepito EnggEcon v.1 15 Methods of Depreciation 1. 2. 3. 4. 5. 6. 7. 8. Straight Line Method Sinking Fund Method Sum of the Years Digit Method Declining Balance Method Double Declining Balance Method Working Hours Method Constant Unit Method Output Method MLMPepito EnggEcon v.1 16 4. Declining Balance Method Declining Balance Method is sometimes called the Constant-Percentage Method or the Matheson formula. The assumption in this depreciation method is that the annual cost of depreciation is the fixed percentage (1 - K) of the Book Value (BV) at the beginning of the year. The formulas for Declining Balance Method of Depreciation are: Annual Rate of Depreciati on(K) 1 - n SV where, SV = FC (1 - K) n FC Book Value = FC (1 - K) m Depreciati on at m th year = FC (1 - K) m -1 (K) Total Depreciati on = FC - SV MLMPepito EnggEcon v.1 17 4. Declining Balance Method MLMPepito EnggEcon v.1 18 4. Declining Balance Method Example: The first cost of a machine is Php 1,800,000 with a salvage value of Php 400,000 at the end of its life of five years. Determine the depreciation after three years using Constant-Percentage Method. Solution: a. Solve for K. Annual Rate of Depreciation(K) 1 - n K 1- 5 SV FC 400,000 1,800,000 MLMPepito EnggEcon v.1 19 4. Declining Balance Method b. Solve for the book value at the end of the third year. BV = FC (1 - K)m BV = 1,800,000 (0.74)3 BV = Php 730,037.21 c. Solve for the total depreciation after three years. Total depreciation = FC - BV Total depreciation = 1,800,000 - 730,037.21 Total depreciation = Php 1,069,962.79 MLMPepito EnggEcon v.1 20 Methods of Depreciation 1. 2. 3. 4. 5. 6. 7. 8. Straight Line Method Sinking Fund Method Sum of the Years Digit Method Declining Balance Method Double Declining Balance Method Working Hours Method Constant Unit Method Output Method MLMPepito EnggEcon v.1 21 5. Double Declining Balance Method The double declining balance depreciation method is a form of accelerated depreciation that doubles the regular depreciation approach. It is frequently used to depreciate fixed assets more heavily in the early years, which allows the company to defer income taxes to later years. DDB Formula: Depreciation at any " nth" year (D n ), 2FC 2 Dn 1 m m 2 BV FC 1 m 2 SV FC 1 m n 1 n m MLMPepito EnggEcon v.1 22 5. Double Declining Balance Method MLMPepito EnggEcon v.1 23 5. Double Declining Balance Method Example: An equipment costs Php750,000 and has a salvage value of Php25,000 after its 25 years of useful life. Using double declining balanced method, what will be the book value of the equipment at the end of 6 years? Solution: 2 BV FC 1 m n 2 BV 750 ,000 1 25 BV Php 454 ,766 .25 6 MLMPepito EnggEcon v.1 24 Methods of Depreciation 1. 2. 3. 4. 5. 6. 7. 8. Straight Line Method Sinking Fund Method Sum of the Years Digit Method Declining Balance Method Double Declining Balance Method Working Hours Method Constant Unit Method Output Method MLMPepito EnggEcon v.1 25 6. Working Hours Method Working Hours Method is a depreciation method that results in the cost basis allocated equally over the expected number of units produced during the period of tangible properties. The formula for Working Hours Method of Depreciation is: Depreciation per hour = (FC - SV) / Total number of hours MLMPepito EnggEcon v.1 26 6. Working Hours Method Example: A machine costs Php 400,000 with a salvage value of Php 200,000. Life of it is six years. In the first year, 4000 hours. In the second year, 6000 hours and 8000 hours on the third year. The expected flow of the machine is 38000 hours in six years. What is the depreciation at the end of the second year? Solution: a. Solve for the depreciation per hour. Depreciation per hour = (FC - SV) / Total number of hours Depreciation per hour = (400,000 - 20,000) / 38000 Depreciation per hour = Php 10 b. Solve for the depreciation at the end of 2nd year. Depreciation = 10 (6000) Depreciation = Php 60,000 MLMPepito EnggEcon v.1 27 Methods of Depreciation 1. 2. 3. 4. 5. 6. 7. 8. Straight Line Method Sinking Fund Method Sum of the Years Digit Method Declining Balance Method Double Declining Balance Method Working Hours Method Constant Unit Method Output Method MLMPepito EnggEcon v.1 28 7. Constant Unit Method Constant Unit Method is the same with Working Hours Method in the structure of the formula. The formula for Constant Unit Method of Depreciation is: Depreciation per unit = (FC - SV) / Total number of units MLMPepito EnggEcon v.1 29 7. Constant Unit Method Example: A coin machine costing Php 200,000 has a salvage value of Php 20,000 at the end of its economic life of five years. Determine the annual reserve for depreciation for the third year only. The schedule of production per year is as follows: MLMPepito EnggEcon v.1 30 7. Constant Unit Method Solution: a. Solve for the total number of coins. Total number of coins =100,000 + 80,000 + 60,000 + 40,000 +20,000 Total number of coins = 300,000 b. Solve for the depreciation per unit. Depreciation per unit = (FC - SV) / Total number of coins Depreciation per unit = (200,000 - 20,000) / 300,000 Depreciation per unit = 0.60 c. Solve for the depreciation reserve for the third year. Depreciation = 0.66 (60,000) Depreciation = Php 36,000 MLMPepito EnggEcon v.1 31 Methods of Depreciation 1. 2. 3. 4. 5. 6. 7. 8. Straight Line Method Sinking Fund Method Sum of the Years Digit Method Declining Balance Method Double Declining Balance Method Working Hours Method Constant Unit Method Output Method MLMPepito EnggEcon v.1 32 8. Output Method The term units-of-output depreciation refers to one of several methods of allocating the cost of an asset over its expected lifetime. The units-ofoutput depreciation method is based on the assumption the asset will output a fixed number of units over its lifetime; therefore, the depreciation expense in a given accounting period is directly related to the asset's output in that same accounting period. Output Method Formula: Units - of - Output Depreciation = (Cost of Asset - Residual Value) Total Units of Output Depreciation Expense = Units of Output Depreciation x Units Produced MLMPepito EnggEcon v.1 33 8. Output Method Example: A company has a machine with a cost of Php 500,000 and a useful life that is expected to end after producing 24,000 units of a component part. Furthermore, the machine's salvage value at that point is assumed to be Php 20,000. Solution: (Cost of Asset - Residual Value) Total Units of Output Php(500,00 0 - 20,000) Units - of - Output Depreciati on = 24,000unit s Units - of - Output Depreciati on = Php20/unit Units - of - Output Depreciati on = MLMPepito EnggEcon v.1 34 References: • LT Blank, A Tarquin. Engineering Economy. McGraw Hill, International Edition, 5th edition, 2002. • William G. Sullivan et al. Engineering Economy.16th Edition. New Jersey: Prentice – Hall,Inc, 2015 • GJ Thuesen, WJ Fabrycky, GJ Thuesen. Engineering Economy. Prentice Hall, Upper Saddle River, NY, 2001. • Chan S. Park. Contemporary Engineering Economics.2nd Edition.USA:Addison-Wesley Publishing Company,Inc. 1997 • Matias A. Arreola. Engineering Economy. 3rd Edition. Philippines: Ken Inc., 1993. • G.J. Thuesen and W.J. Fabrycky. Engineering Economy.8th Edition. New Jersey: Prentice – Hall, Inc., 1993 • Max Kurtz. Engineering Economics for Professional Engineers’ Examination.2nd Edition. New York: McGraw-Hill, 1975 MLMPepito EnggEcon v.1 35 Thank you! MLMPepito EnggEcon v.1 36