固定資產(chǎn)折舊管理(英文)

1、DepreciationBy:John Powell and Alan SunMathematics of FinanceDr. Janusz KawczakAbstractDepreciation is the decline in value of an object over time and can be calculated in many different methods. However, these methods are all estimates of an objects value or“ Book Value ” ,and can differ widely. Du

2、e to the importance of Depreciation in today s financial world, wedecided to utilize each method of Depreciation and find the most effective method. To achieve this, we used a test case and used its variable to find the annual depreciations that would occur for each method. Once the results were fou

3、nd, the comparison showed that the Straight Line Method of Depreciation, where there is an uniform annual decline of value over a set period of time, is the most efficient and beneficial method. This conclusion reinforces the current beliefs in the financial world.BackgroundDepreciation is the term

4、used to describe the decline in value of a physical asset over a certain span of time. Most objects lose value as they are used due to damage from use, aging, obsolescence, and impairment. However the exact amount of value that is lost and the current “ book value ” of an asset cannot be easily know

5、n. Depreciation is thus used as an estimate of this decline and is used for several important purposes in today s business world.Depreciation has been a factor in human economics ever since the advent of trade. At its most basic, depreciation states that an older object is usually not as valuable as

6、 a newer one. However, with the formation of large corporations and the creation of our modern economic structure, depreciation has taken on a greater importance with a genuine need for accurate calculations of depreciation.Today most companies need a precise estimate of their physical assets deprec

7、iation for two main reasons. First, companies must compare the expenses in using and buying equipment and materials to the revenue generated in that year. Without an accurate estimate for depreciation, a company s profit ancdurrent value could not be known. Secondly, companies must ascertain the val

8、ue of their assets and determine that objects are not appraised as being more costly than their actual worth. In fact, the value of such assets directly affects the taxes that must be paid each year and depreciation is used to find the exact amount that is deductible.The exact amount depreciated ann

9、ually is based on several factors. The main criteria is the method used in assessing an object's depreciation. The main methods range from deducting a set amount for a certain period of time to evaluating the exact hours that and object is used to generate revenue. Also, different physical asset

10、s can be evaluated in drastically dissimilar manners. In the United States, objects can have a depreciable life span ranging from 5 years to 50 years or more depending on several factors. For example, computers and electronics that becomeobsolete quickly will undergo faster depreciation than trucks

11、or factories that have much longer life-spans. Most countries today have set laws and regulations that determine the calculation of depreciation. In America, the law uses Straight Line along with Declining Balanace as an orthodox measure to make sure that all the companies and corporations in the Un

12、ited States conform with each other when reporting their company' s data and filing their tax reports.Research ProblemDepreciation has become a complex operation in todays business world. With ourcurrent economical situation, the precise estimate of capital and assets becomes crucial. Still, the

13、re are many differing ways of calculating depreciation, ranging from the simplistic straight line, to amortization that includes monetary inflation. Using a specific method can result in drastically different results, and there can be methods that are more beneficial to a company. In fact, the prope

14、r method of depreciation can lower taxable income and portray larger assets. We thus decided to research the methods of depreciation and determine which one creates the best results. Through setting up a test case and calculating depreciation for each different type we can discover the method that a

15、meliorates a company' s financial situationMethods for Finding Depreciation 1.1- Straight-Line Method The Straight-Line Method is the most popular and simplistic way to find depreciation. In this method, it is assumed that depreciation occurs at a constant rate per unit of time. The constant rat

16、e yields a linear equation appearing as straight line when graphed. In Eq. 1 R is the depreciation allowance, W is the wearing value, which is original value minus scrap value, and n is the number of useful years that the item can be used. Below is a Basic Notation for Depreciation table. (Guthrie,

17、2004)WdR 一1Basic Notation for DepreciationC Original cost of the capital assetS Scrap ValueW Wearing Value, W C SRt Depreciation allowance for year tBt Book Value at the end of year tr Depreciation rate per year, per service hour, or production unit.n Useful life of capital asset in years, service h

18、ours, or production units Example 1.1: Your family buys a car for $20,000 and it has an estimated life of 8 years with a trade in value of $3,500. Find the straight-line depreciation allowances and make a schedule.W 20,000 3,500 16500R $2062.500$20,000.001$2,062.50$2,062.50$17,937.502$2,062.50$4,125

19、.00$15,875.003$2,062.50$6,187.50$13,812.504$2,062.50$8,250.00$11,750.005$2,062.50$10,312.50$9,687.506$2,062.50$12,375.00$7,625.007$2,062.50$14,437.00$5,562.508$2,062.50$16,500.00$3500.00In the example above the car depreciates at a rate of $2062.50 a year for 8 years. Each year the car depreciates b

20、y another $2,062.50 until it is traded in at the end of the eight year for $3,500.The car is not always traded in at the end of its“ estimated “ life but can be used for longer peHowever its “ book value “ remains at $3,500.1.2- Service Hours MethodThe Service Hours Method is similar to the Straight

21、- Line Method except it calculates” bookvalue “ based on the hours an object has been used instead of set amount of depreciationeferh year. When using this system of depreciation a company has to keep up with all of the hours of usage so that it can calculate the correct depreciation amount. This ma

22、kes it much more difficult to obtain than the straight-line method and makes it a lot less practical in real life. (Guthrie 2004).RtrH t2In Eq. 2 Rt is the depreciation allowance for year t, r is the rate in dollars per service hour,H t represents the service hours expended in year t. (Guthrie 2004)

23、.1.3- Production Units MethodThe Production Units Method of depreciation uses the number of actual units produced to determine the depreciation allowance. To get the depreciation allowance the depreciation rate is multiplied by the number of items produced. This method works well when factory produc

24、tion is up because when a company produces more they can write off larger amounts as depreciation. This method is also very similar to the straight-line method except that n is the estimated life in units produced and the rate of depreciation is expressed in dollars per unit. (Book Depreciation 2004

25、-2005)RtrUtIn Eq. 3 r is the rate in dollars per unit, Ut are the number of output units. (Guthrie 2004).2.1-Sum of the Year ' s DigitsThe Sum of the Year ' s Digits method is a way to calculate depreciation where the depreciation rate diminishes as it gets closer to the end of the estimated

26、 life of the item. To calculate the rate of depreciation the number of years of the estimated life of the item are added up and placed in the denominator and the numerator is the number of years that are left in the items estimated life. Then the rate of depreciation is multiplied by the wearing val

27、ue to get the depreciation value. Below is Eq. 4 which shows the depreciation formula. (Depreciation Schedule 2004-2005)nn 11r1 , 12 , rn 1 2 . n 1 2 . n1 2 . nRtrW4In Eq. 4 rt is the depreciation rate per year andW is the wearing value.Example 2.1: A clothing company buys several cash registers for

28、 $5,000 each. Each cash register has an expected life of 6 years with a trade-in value of $900. Find the sum of the year depreciation and make a schedule.Wearing Value: W C S $5,000 $900 $4,100Denominator of the Depreciation Rate: 1 2 . 6 216八一 5八_RtrWVR1$4,100$1171.43R2一 $4,100$976.19, and so on.21

29、210$5,000.001$1,171.43$1,171.43$3,828.5723456$976.19$780.95$585.71$390.48$195.24$2,147.62$2,928.57$3,514.28$3,904.76$4,100$2,852.38$2,071.43$1,485.72$1,095.24$9002.2 Declining Balance MethodThe Declining Balance Method of depreciation uses a fixed rate of depreciation that is multiplied by the book

30、value to get the depreciation allowance. In this formula the depreciation rate stays constant but since the depreciation allowance depends on the book value as well, the amount of money that is depreciated changes at every step. The larger amounts of depreciation will takeplace in the first few year

31、s and gradually the amount of depreciation will get smaller and smaller.The rate will be a percentage of the straight-line rate so r is equal to 1/n. Typical rates ofwhich calculates thedepreciation are 150% and 200%. 200% depreciation is called the double declining balance because the rate isr = 2(

32、1/n) . Double declining balance gives an accelerated write-off but doesn ' t take the book value to scrap value. For this reason the last two or three years of depreciation are calculated with the straight-line method. Below is Eq. 5 depreciation allowance at the end of the year t. (Declining Ba

33、lance 2005)Rt2/n Bt 1Book Value Perspective: RBt 1Bt3.1- Amortization of Total DepreciationAll of the methods of depreciation that we have seen so far haven' t taken into account the tim(value of money. This method of depreciation assumes that the amount you paid for the item grows over time and

34、 each successive book value estimate will gain interest. In this method the depreciation allowances are like rent and are subtracted from the present value like an ordinary annuity. Because this method is like an ordinary annuity the depreciation allowances will all be constant. Below is Eq. 6 which

35、 is used to calculate the depreciation allowances. (Guthrie 2004)aniEx. 3.1: The School of Fine Arts is buying new drawing tables for the students at a cost of $10,000 and they have a life expectancy of 5 years with a trade in value of $2,000.Find the annual depreciation allowances using the amortiz

36、ation of total depreciation method and assuming an investment rate of 6%(1).n5C S(1 i)Rani $10,000 $2,000(1.06)Ra56%$8505.48 Ra56%R $2355.703.2- Sinking Fund MethodIn the Sinking Fund Method of depreciation it is assumed that there is a savings account set up to replace an asset at the end of its li

37、fe. The target value is equal to the wearing value and the depreciation allowances consist of the payment for the fund and the interest that it collects. Gradually as this method moves on the depreciation allowances will get marginally larger. The formula for the deposit into the fund is calculated

38、by using the future value of an ordinary annuity.Below is Eq. 7 which is the formula for calculating depreciation through the sinking fund method. (Guthrie 2004)RtC S t 11 iSniResultsThe problem below will be calculated using several different methods to compare the depreciation allowances between t

39、he different methods. When we compare the depreciation allowances and the difficulty of solving the depreciation allowances we will determine which methods work best and why companies use these methods.A paper mill that operates 24 hours everyday, 365 days a year, buys a new tree grinder for $1,000

40、with an estimated life of 5 years (8,760 hours a year) with a trade-in value of $200. Calculate the depreciation using different methods. (For the Service Hours Method it has a useful life of 54,750 hours and for Amortization of Total Depreciation the interest rate is 5%)Straight-Line MethodW $1,000

41、 $200R - $160 per year depreciationn501$160$160$1,000 $8402$160$320$6803$160$480$5204$160$640$3605$160$800$200Service Hours Method43,800r W $1,000 $200 1.83 0per hour$0.0183*8,760$160 per year depreciation01$160$160$1,000 $8402$160$320$6803$160$480$5204$160$640$3605$160$800$200Sum of the Year '

42、s DigitsWearing Value: W C S $1,000 $200 $800Depreciation rate denominator: 1 2 . 5 15R1 $800$266.67, ,R $800$213.33, and so on.1515012345$266.67$213.33$160.00$106.67$53.33$266.67$480.00$640.00$746.67$800.00$1,000$733.33$520.00$360.00$253.33$200.00Amortization of Total DepreciationnC S 1 iRani$1,000

43、 $200(1.05)5 Ra55%$1,000 $156.71Ra55%$843.29 Ra55%R $194.7801$194.78$194.78$1,000$805.222$194.78$389.56$610.443$194.78$584.34$415.664$194.78$779.12$220.885$20.88$800.00$200.00Depreciation Method ComparisonBook Value口 Straight Line Method Service Hours Method口 Sum of the Year ' s Dig口 Amortizatio

44、nYearstsYearsSum of the Year s DigitseHrav kooBStraight Line Method/ Service Hours Method123456eHrav kooBYearsAmortization120010008006004002000123456ConclusionAfter our example analysis and research of contemporary practices we concluded that the Straight Line Depreciation method is the best method

45、of depreciating assets for multiple reasons. When used in conjunction with the other methods, Straight Line Depreciation gives consistent results that also are much easier to calculate and obtain in the real world. However, the different methods can not always be directly compared as their yearly de

46、preciation has inherent differences based on the method they re calculated. For example, when using Amortization to depreciate an object s value, there is the additional factor of interest that is not present in Straight Line Depreciation or other similar methods.s worthHowever, it is still possible

47、 to compare some of the data, and through the summation of the Book Values, we can find the total amount an asset contributes to a company span of five years. To find this you just useBVT BV1 BV2 BV3 BV4 BV5ex:1000 840 680 520 360 200 $3,600Using this you obtain:Straight Line Method: $3,600.00Servic

48、e Hours Method: $3,600.00Sum of the Year s D$ig3it0s6: 6.66Amortization: $3252.20Thus as seen from these calculations it isevident that the total summation of this specific asset book value for five years can change greatly when differing methods are used. For example, when comparing Amortization to

49、 Straight Line Method the difference can be seen as:BVStraightLineBVAmortization $3600 $3252.20$347.80This means that the company is valued lower by $347.80 over the span of five years when Amortization is used to depreciate the asset instead of straight line method. Similarly, using the Sum of the

50、Year s Digits method also results in a much smalslert avsalue for five years with an even larger difference:BVStraightLineBVSumYearsDigits$3600 $3066.66 $533.34With these two comparisons, it is seen that the more exponential decline in value that occurs with Amortization and Sum of the Year s Digits results in much lowelureasfosrethveafirst fewyears. Us