Chapter 5 Depreciation PDF

Pamantasan ng Lungsod ngMaynila College of Engineering and Technology ENGINEERING ECONOMICS Chapter 5 Depreciation Prepared by: Engr. Jenalyn Macarilay Electronics Engineering Department Learning Outcomes Define and un...

Pamantasan ng Lungsod ngMaynila College of Engineering and Technology ENGINEERING ECONOMICS Chapter 5 Depreciation Prepared by: Engr. Jenalyn Macarilay Electronics Engineering Department Learning Outcomes Define and understand the concept of depreciation Define and recognize different methods in solving depreciation problems: Straight Line Method (SLM), Declining Balance Method (DBM), Double Declining Balance Method (DDBM), Sinking Fund Method (SFM), Sum-of-the- Year’s Digit method (SOTYDM), and Output Method Solve real life and practical problems involving Straight Line Method (SLM), Declining Balance Method (DBM), Double Declining Balance Method (DDBM), Sinking Fund Method (SFM), Sum-of-the- Year’s Digit method (SOTYDM), and Output Method  DEPRECIATIO N the decrease in the value of physical property with the passage of time used for internal accounting to track value of assets  VALUE In a commercial sense, is the present worth of all future profits that are to be received through ownership of a particular property  VALUE  Sometimes called the amount which a willing The value which is usually depreciated book value buyer will pay to a willing determined by a The worth of a property as seller for the property where disinterested third party in shown on the accounting each has equal advantage order to establish a price records of an enterprise and is under no compulsion that is fair to both seller and to buy or sell buyer BOOK MARKET FAIR VALUE VALUE VALUE What the property is worth to  The amount of the property  Also called resale value the owner as an operating would sell for if disposed off The price that can be unit as a junk obtained from the sale of the property after it has been used Salvage year is the time when the scrap value is equal to the book value SCRAP SALVAGE USE VALUE VALUE VALUE  a. Normal depreciation 1.Physical Is due to the lessening of the physical ability of a property to produce results Common causes are wear and deterioration 2. Functional TYPES Due to the lessening in the demand for the function which the property was OF designed to render Common causes are inadequacy, DEPRECIATI changes in styles, saturation of markets or more efficient machines are produced ON b. Depreciation due to changes in price levels Almost impossible to predict and therefore is not considered in economy studies c. Depletion Refers to the decrease in the value of a property due to the gradual extraction of its contents. PHYSICAL LIFE The length of time during which it is capable of performing the function for which it was designed and manufactured ECONOMIC LIFE The length of time during which the property may be operated at a profit  useful life of the property in L years the original cost Co the value at the end of life, CL the scrap value (including gain or loss due to removal) SYMBOL the annual cost of d depreciation S the book value at the end of Cn n years Total depreciation up to age Dn n years Depreciable year n  Total hours of economic life H the hours the hn asset has been SYMBOL used S Total output produced in its N economic life the output produced in Nn the depreciable  DEPRECIATION METHODS STRAIGHT LINE METHOD (SLM) DECLINING BALANCE METHOD (DBM) DOUBLE DECLINING BALANCE METHOD (DDBM) SINKING FUND METHOD (SFM) SUM – OF-THE-YEARS METHOD (SOTYDM) SERVICE-OUTPUT METHOD HOUR OUTPUT METHOD  STRAIGHT LINE METHOD This method assume that the loss in value is directly proportional to the age of the property 𝑪𝑶 −𝑪 𝑳 𝒏 ( 𝑪 𝑶 − 𝑪 𝑳) 𝒅= 𝑫 𝒏= 𝑳 𝑳 𝑪𝒏 = 𝑪 𝑶 − 𝑫 𝒏  STRAIGHT LINE METHOD Sample Problem An electronic balance costs P90,000 and has an estimated salvage value of P8,000 at the end of its 10 years lifetime. What would be the book value after three years, using straight line method in solving for the depreciation? Given: L = 10 years CL = P8,000 Co = P90,000 Required: C3 Solution: Ans. = P65, 400  Example 1 Equipment bought for P60, STRAIGH 000 is expected to last for 30 years. If the book value T LINE after 20 years is P20,000. How much is the METHOD depreciation each year, and the book value after 10 years.  Example 2 Prepare a depreciation table for an asset bought at P150,000 and STRAIGH estimated to be useful T LINE for a period of 5 years. Estimated salvage METHOD Yeavalue r Beginning is Value Book 10% Depreciat of ion Book its Value 1 original 150,000 cost. 2  DECLINING BALANCE METHOD  Sometimes called the constant percentage method or the Matheson formula  It is assumed that the annual cost of depreciation is a fixed percentage of the salvage value at the beginning of the year  The ratio of the depreciation in any year to the book value at the beginning of that year is constant throughout the life of the property and is designated by k, the rate of depreciation  This method does not apply if the salvage value is zero, because k will be equal to one and d will be equal to Co. DECLINING BALANCE METHOD  DECLINING BALANCE METHOD Sample Problem An electronic balance costs P90,000 and has an estimated salvage value of P8,000 at the end of its 10 years lifetime. What would be the book value after three years, using declining balance method in solving for the depreciation? Given: L = 10 years CL = P8,000 Co = P90,000 Required: C3 Solution: Ans. = P43, 536.3  Example 1 A machine worth 800,000 is brought from china, freight charges amount to 200,000. If the scrap DECLININ value of the machine is G 50,000 that occurs at BALANCE the end of 17 years. METHOD (a) compute the depreciation at the end of the year11 (b) Compute the book value at the end of 11 years  Example 2 A certain type of machine loses 10% of its value each year. The machine costs DECLININ P2,000 originally. Make out a schedule showing the yearly G depreciation, the total BALANCE depreciation and the book value Initialat Depreciat the endTotal of each METHOD Year year for 3 years. Book Value ion Deprecia tion Boo k Valu e 1 2,000 2  DOUBLE DECLINING BALANCE METHOD  This method is very similar to declining balance method except that the rate of depreciation k is replaced by 2/L.  The salvage value should not be subtracted from the first cost when calculating the depreciation charge. DOUBLE DECLINING BALANCE METHOD  DOUBLE DECLINING BALANCE METHOD Sample Problem An electronic balance costs P90,000 and has an estimated salvage value of P8,000 at the end of its 10 years lifetime. What would be the book value after three years, using double declining balance method in solving for the depreciation? Given: L = 10 years CL = P8,000 Co = P90,000 Required: C3 Solution: Ans. = P46, 080  Example 1 Determine the rate of depreciation, the total DOUBLE depreciation up to end DECLININ of the 8th year and the book value at the end of G 8 years for an asset BALANCE that costs P15,000 new METHOD and has an estimated scrap value of P2,000 at the end of 10 years by double declining balance method.  Example 2 A certain type of machine DOUBLE loses 5% of its value each year. The machine costs DECLININ P2,000 originally. Make out a G schedule showing the yearly depreciation, the total BALANCE depreciation and the book METHOD value Year Initialat Depreciat the endTotal year for 3 years. Book ion of each Deprecia Boo k Value tion Valu e 1 2,000 2  SINKING FUND METHOD This method assumes that a sinking fund is established in which funds will accumulate for replacement. The total depreciation that has taken place up to any given time is assumed to be equal to the accumulated amount in the sinking fund at that time  SINKING FUND METHOD 𝒅= ( 𝑪 𝟎 − 𝑪 𝑳 ) [ 𝒊 𝑳 ( 𝟏+ 𝒊 ) − 𝟏 ] [ ] 𝒏 ( 𝟏+𝒊 ) − 𝟏 𝑫 𝒏= ( 𝑪 𝟎 − 𝑪 𝑳 ) 𝑳 ( 𝟏+𝒊 ) − 𝟏  SINKING FUND METHOD Sample Problem An equipment costs P10, 000 with a salvage value of P500 at the end of 10 years. Calculate the annual depreciation by SFM at 40% interest. Given: L = 10 years CL = P500 Co = P10,000 i= 40% Required: d Solution: Ans. = P136.08  Example 1 A firm bought an equipment fee for P56,000. Other expenses including SINKING installation amounted to FUND P4,000. The equipment is expected to have a METHOD life of 16 years with a salvage value of 10% of the original cost. Determine the book value at the end of 12 years by straight line methods and sinking fund methods at 12% interest.  Example 2 Prepare a depreciation table SINKING for an asset that was bought at P150, 000 and estimated to be useful for a period of 7 FUND years. Estimated salvage value is 10% of its original METHOD cost. Money is worth 10% CA.Initial Year Book Depreciat ion Total Deprecia Boo k Value tion Valu e 1 150, 000 2  SUM OF THE YEAR’S DIGIT METHOD This method uses the year’s digit (in reverse order) in computing for the depreciation. Sum of the years Digit: Sum of the Reverse Digits from L to (L+1-n): SUM OF THE YEAR’S DIGIT METHOD 𝒅𝒏 =( 𝑪 𝟎 − 𝑪 𝑳 ) [ 𝟐( 𝑳+𝟏 − 𝒏) 𝑳( 𝑳 +𝟏) ] )[ ] 𝒏(𝟐 𝑳 +𝟏− 𝒏) 𝑫 𝒏= ( 𝑪 𝟎 − 𝑪 𝑳 𝑳( 𝑳+𝟏)  SUM OF THE YEAR’S DIGIT METHOD Sample Problem An industrial plant bought a generator set at P90, 000. other expenses including installation amounted to P10,000. The generator set is to have a life of 17 years with a SV of P5,000. Determine the book value at the end of 13 years using SOTYDM. Given: L = 17 years CL = P5,000 Co = P90,000 Installation Fee=P10, 000 n = 13 years Required: C13 Solution: Ans. = P11, 209.15 -  Example 1 A telephone company purchased a microwave SUM OF radio equipment P6,000,000. Freight and for THE installation charges YEAR’S amounted to 3% of the DIGIT purchased price. If the quipment shall be METHOD depreciated over a period of 8 years with a SV of 5%, determine the depreciation charge on the 5th year using SOTYDM  Example 2 A structure costs P12,000 new. It is estimated to have a SUM OF new life of 5 years with THE a salvage value at the YEAR’S end of life of P1,000. DIGIT Determine the book value Year at theDepreciat Initial end ofBoo each METHOD Book year ofValue life. ion k Valu e 1 12, 000 2  HOUR OUTPUT METHOD This method assumes that depreciation that is directly proportional to the period the asset has been used and the depreciable amount wherein the constant of proportionality is the reciprocal of the economic𝒉 𝒂 life. 𝑪𝒏 =𝑪𝟎 − 𝑫𝒏 𝒅𝒏 = ( 𝑪𝟎 − 𝑪 𝑳) 𝑯  SERVICE OUTPUT METHOD This method assumes that the total depreciation that has taken place is directly proportional to the quantity of output of the property up to that time. Has the advantage of making the unit cost depreciation constant and giving low depreciation expense during periods of low production 𝑵𝒂 𝑪𝒏 =𝑪𝟎 − 𝑫𝒏 𝒅𝒏 = ( 𝑪 𝟎 − 𝑪 𝑳) 𝑵 SUM OF THE YEAR’S DIGIT METHOD 𝒅𝒏 =( 𝑪 𝟎 − 𝑪 𝑳 ) [ 𝟐( 𝑳+𝟏 − 𝒏) 𝑳( 𝑳 +𝟏) ] )[ ] 𝒏(𝟐 𝑳 +𝟏− 𝒏) 𝑫 𝒏= ( 𝑪 𝟎 − 𝑪 𝑳 𝑳( 𝑳+𝟏) Sample Problem A Television Company purchased machinery for P100,000 on July 1, 1979. It is estimated that it will have a useful life of 10 years; scrap value of P4,000, production of 400,000 units and working hours of 70, 000. The company uses the machinery for 8,000 hours in 1979 and 7,000 hours in 1980. The machinery produces 36,000 in 1979 and 44,000 units in 1980. Compute the depreciation in 1980 using service- output and hour-output method. Given: L = 10 years CL = P4,000 Co = P100,000 N=400, 000 units N1980= 44, 000 units H=70, 000 hours h1980= 7, 000 hours Required: d1980 Solution: Ans. SOM: P10, 560  Example 1 An electric bulb bought for P100 is guaranteed HOUR to be used for 50 hours. The certain company OUTPUT uses the said bulb 10 hours a day. If there is METHOD no scrap value for the bulb, compute the daily depreciation, and create the depreciation table throughout its economic life  Example 2 A tire bought for P1, 000 is expected to be useful in travelling SERVICE 100km aftrer which it can be sold as a scrap OUTPUT for P50.00. (a). The pedometer METHOD displays a value of 85km, what is the book value of the tire? (b). How much did the owner need to travel for the tire to amount to P80.00?  REFEREN CES o Engineering Economy, Blank and Tarquin, 7th Edition, McGraw-Hill, 2012 o Engineering Economy, Hipolito Sta. Maria o Various online materials THANK YOU