Special Topics ISYE 4803
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This 0 page Class Notes was uploaded by Maryse Thiel on Monday November 2, 2015. The Class Notes belongs to ISYE 4803 at Georgia Institute of Technology - Main Campus taught by Steven Hackman in Fall. Since its upload, it has received 20 views. For similar materials see /class/234187/isye-4803-georgia-institute-of-technology-main-campus in Industrial Engineering at Georgia Institute of Technology - Main Campus.
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Date Created: 11/02/15
Depreciation A Tax Effect of Depreciation 1 For the current year a company has income of R and cost of C for a net income before tax of RC for the year The company s marginal tax rate is T The company s aftertax cash ow for the year is therefore 1 TR 7 C Example I Say R 3000 and C 1000 with T 40 Then the company s aftertax cash ow for the year is 1 7 0403000 7 1000 1200 Note that this may be equivalently expressed as 0603000 7 0601000 1800 7 600 1200 That is the company receives a net of 60 cents for each dollar of revenue it takes in but it only costs the company 60 cents for dollar of expense On the expense side note that 139cC 7 C EC 7 10000401000 and so the net effect of being able to deduct expenses it that the company receives a tax bene t of 17C 400 ie it wrote a check for 1000 during the year and receives back 400 due to the expense writeoff 2 Let s assume the revenue R is suf ciently high to offset the expenses In what follows we shall ignore the aftertax cash ow due to revenue since it is a constan as far as the analysis of the aftertax cash ow due to cost Now let s suppose for the current year a company spends I 1000 on capital investment for equipment The equipment is classi ed as 5year property and straightline depreciation is used If the company were able to writeoff this capital investment as an expense then the aftertax cash ow would be 7600 exactly as in Example 1 However the govemment s perspective on this is that the equipment is being used over a 5 year period and provides economic value over its entire book life of 5 years The company may choose to use this equipment for more than 5 years Consequently the government will only allow the company to expense each year an appropriate amount for the wear and tear or depreciation of the equipment Since straightline depreciation is being used the depreciation expense each year is 10005 200 There is NO outofpocket depreciation expense each year That is the 1000 is spent now the 200 is computed only for tax purposes As explained in 1 above from the aftertax cash ow perspective this 200 depreciation allowance yields a tax bene t of 040200 80 each year for the next 5 years That is the aftertax cash ow due to the capital investment for the next 5 years ignoring the salvage value due to possible sale of equipment is lo I2 l3 I4 Is 1 1000 80 80 80 80 80 Note how the undiscounted sum of the depreciation allowances over the 5year horizon adds up to 400 the total tax bene t Again the total tax bene t of 400 would be added to the 71000 if this were an ordinary expense for materials labor etc Suppose the company were to use a 6 cost of capital for purposes of determining the Net Present Value of this cash ow stream then the NW 7 1000 17106395006 80 7 1000 421280 7 66301 which translates to a net cost of 663 per dollar spent on this capital equipment Note that if this equipment had been eXpensed then the net cost would be 60 per dollar spent The loss of 63 is due to the DELAY of receiving the bene t of 80 per year for 5 years as above as opposed to receiving the total of 400 right NOW Which cash ow would a company prefer For the purpose of aftertaX cash ow the company would prefer to be able to writeoff as much depreciation as quickly as it can That is it would prefer accelerated depreciation For the purpose of reporting pro ts however the company would prefer to delay the eXpense The IRS allows a company to keep two sets of books one for taX purposes and the other for reporting to shareholders B Accounting for Depreciation in the Income Statement Example 2 Suppose our company has a net operating income R 7 C for the year of 3000 and a depreciation eXpense of 1000 According to what we have learned above the taxes owed to the government this year would be 0403000 7 1000 800 The Flow In is therefore 3000 and the Flow Out is 800 for a net of 2200 Here is the income statement approach to this calculation In general notation the two approaches to after taX cash ow are respectively Income Statement Approach 1 TR 7 C 7 Dep Dep 1 TR 7 C T Dep Flow In 7 Flow Out Approach R 7 C TR 7 C 7 Dep 1 TR 7 C T Dep which produce the same result as it should Note that if the depreciation adjustment below the line ie below the Net Income after taX is NOT made then the income statement approach would incorrectly report an after taX cash ow of 1200 The discrepancy would arise because the depreciation allowance is NOT an out of pocket eXpense