Slide Set 9 Depreciation and After-tax analysis

1. 1 Slide Set 9 – Depreciation and After-tax analysis IEM 3503/IEM3513 Dr. Baski Balasundaram Industrial Engineering & Management

2. 2 Chapter Outline

3. 3 Depreciation Terminology Depreciation is the reduction in value over time of an asset. Brought on by: Wear/Usage; Deterioration; Obsolescence. Book Depreciation – used by businesses for internal accounting purposes Tax Depreciation – used in tax calculations according to government regulations.

4. 4 Important Terms First Cost or Unadjusted Basis - B Initial purchase price + all costs incurred in placing the asset in service Book Value - BVt Remaining undepreciated capital investment on the books after total amount of depreciation charges to date have been subtracted from the basis. Recovery Period – n Depreciable life of the asset in question – often set by law.

5. 5 Important Terms

6. 6 Depreciation Methods Classical methods for book depreciation Straight Line (SL) Model Declining Balance (DB) Model Modified Accelerated Cost Recovery System (MACRS) Methods Method for tax depreciation acc. US law. Acceptable for book depreciation also.

7. 7 Book value Curves for Different Depreciation Models

8. 8 Straight Line (SL) Depreciation A fixed amount is removed each year by depreciation

9. 9 Straight Line (SL) Depreciation

10. Example Basis, B = 50K, Salvage S=10K, 5 year depreciable life. Find the annual straight line depreciation, and depreciation rate Dt = D = (B-S)/n = (50K – 40K)/5 = 8K dt = d = D/(B-S) = 1/n = 0.2 SL equation is BV = 50K-t*8K 10

11. 11 Declining Balance (DB) Depreciation A fixed percentage is removed each year by depreciation DB is an accelerated depreciation method Provides greater depreciation amounts in the early time periods over straight line Fixed percentage (OR) Uniform percentage method

12. 12 Declining Balance (DB)

13. 13 Declining Balance (DB)

14. 14 Double Declining Balance (DDB)

15. Comparison- DB and DDB Consider an asset with basis value B= 80K. Compare the BV curves when it depreciates by DDB method, and DB method with d=0.1 and DB with d=0.05. Assume a 10 yr life. 15

17. 17 Example A fiber optics testing device has a first cost of $25,000 and a useful life of 12 years. (a) Calculate the depreciation, depreciation rate and book value for year 4 if DDB is to be used. (b) Calculate the depreciation and book value for year 4 if DB method is used and a salvage value of $2500 after 12 years is estimated.

18. Example (a) B=25K, n=12. DDB ? d = 2/n = 1/6 BV4 = B(1-d)4 = $12.06K D4 = d * BV3 = d*B(1-d)3 = $2.41K d4 = D4 / B = d*(1-d)3 = 0.096 (b) DB, S is given at 12, need d: S = B(1-d)12 ? d = 1- (S/B)(1/12) = 0.175 BV4 = B(1-d)4 = $11.58K D4 = d * BV3 = d*B(1-d)3 = $2.46K d4 = D4 / B = d*(1-d)3 = 0.098 18

19. 19 Modified Accelerated Cost Recovery System (MACRS) MACRS was derived from the 1981 ACRS system and went into effect in 1986. Defines statutory recovery (depreciation) percentages. Percentages were derived from the DDB method with a switch to SL at the optimal time. Assumes half year convention – assets placed in service mid-year.

20. 20 Modified Accelerated Cost Recovery System (MACRS)

22. Example A company is purchasing a surface mount placement machine. First cost including installation will be $98,000 with an estimated salvage value of $7000 at the end of its projected useful life of 7-years. By MACRS property classification, this is a 5-year property. What is the depreciation charge in each year of its depreciable life by the MACRS model. 22

23. Example (e.g. 6.9) 23

24. 24 Income Tax Terminology and Relations for Corporations (and Individuals) Gross Income (GI) Total income for the tax year from all revenue producing function of the enterprise Sales revenues, Fees, Rent, Royalties, Sale of assets Income Tax The total amount of money transferred from the enterprise to the various taxing agencies for a given tax year

25. 25 Terms - continued Operating Expenses (E) All legally recognized costs associated with doing business for the tax year Real cash flows that are tax deductible for corporations: Wages and salaries, Utilities, etc. Taxable Income Calculated amount of money for a specified time period from which the tax liability is determined TI = Gross Income – expenses – depreciation TI = GI – E – D

26. 26 Terms - continued Tax rate (T) A percentage of TI owed in taxes The applicable tax rate depends upon the total amount of TI Taxes owed equals: Taxes = (TI)(T) Net Operating Profit After Tax (NOPAT) NOPAT = TI – (TI)(T) = (TI)(1-T)

27. 27 U.S Federal Corporate Tax Rates (2003)

28. 28 Effective Tax Rate Graduated tax rate system Marginal tax rates Change with TI ranges, so Taverage = Taxes/TI Effective Tax Rate used in our analysis is also a single number, that also includes state tax rate. Calculated as: Te = Tstate average + (1- Tstate average)(Tfederal average) So, Taxes = (TI)(Te)

29. 29 Before-Tax and After-Tax Cash Flow NCF = cash inflows – cash outflows Cash Flow Before Tax (CFBT) CFBT = gross income – expenses = GI – E* If the year includes first cost or salvage value, the expression will be a bit different Cash Flow After Tax (CFAT) CFAT = CFBT – Taxes = CFBT – (TI)(Te) CFAT = (GI – E) – (GI – E – D)(Te) CFAT = (GI – E)(1-Te) + D(Te) (GI-E) is what we would call NCF, but taking taxes into account reduces it. Depreciation is not a real cash flow, but it has a “positive” effect!

30. 30 Effect of Depreciation Methods on Taxes Given recovery period n, choosing the depreciation rates that minimize the PW of taxes paid is obviously preferable That’s why there is a standardized depreciation model (MACRS) that must be used! Minimizing the PW taxes is equivalent to maximizing the present worth of depreciation

31. 31 Comparing Depreciation Methods Assumptions Effective Tax rate is a constant CFBT exceeds annual depreciation under all methods All depreciation methods reduce BV to S in n years Consequences The total taxes paid (sum of all taxes over 1..n ignoring time value of money) are equal for all depreciation models The PW of taxes paid is less for accelerated depreciation methods Note: For a fixed depreciation method and varying n, PWtaxes is less for smaller n values

32. 32 Capital Gains/Losses for Capital assets Capital assets: Examples include stocks, bonds, real property used in the production of income, not used in trade It is important to determine whether something qualifies as a capital asset, and if they receive preferential treatment in the current tax system Specifically excluded are, machinery, plant and equipment Selling price is SP and first cost is P Capital Gain (CG) if SP > P CG = SP – P Capital Loss (CL) if SP < P CL = P – SP Often not applicable to engineering econ. analysis!

33. 33 Section 1231 property Gains, Losses and Depreciation Recapture Selling price is SP, Book value by MACRS is BVt and initial investment is P For Depreciating assets Depreciation Recapture (DR) if BVt < SP < P DR = SP – BVt DR and Sec. 1231 Gain (SG) if SP > P DR = P-BVt and SG = SP - P Sec. 1231 loss (SL) if SP < BVt SL = BVt – SP For Non-depreciating assets Sec. 1231 Gain (SG) if BVt < SP, SG = SP – BVt Sec. 1231 Loss (SL) if BVt > SP, SL = BVt - SP

34. 34 General TI Equation The year an asset is disposed, the taxable income TI needs to be calculated depending on the nature of the asset using one of the following expressions The basic TI equation for capital assets: TI = GI – E – D + CG – CL Obviously, only one of CG or CL will exist The basic TI equation is Sec 1231 property: TI = GI – E – D + SG + DR– SL Either we have SG and DR, or We have SG, or We have SL

35. 35 After-Tax analysis Work with CFAT instead of NCF in all your economic analysis Use market-MARR = MARR + f + MARR*f to account for the effects of inflation See examples 6.31,32, 33 to understand the impact of taxes on economic decisions, and common mistakes that are committed when inflation is not properly taken into account

36. Example 6.33 First cost is $98,000 with an estimated salvage value of $7000 after a useful life of 7 years. Machine classifies as a 5yr-asset under MACRS. Assume a market MARR of 15% per year and an annual inflation rate of 6%. Annual savings from using this machine in year 1 is $20,350 and increasing at 10% per year. Carry out an after-tax analysis at an effective tax rate of 35% to determine if this project is viable. Section 1231 gains/losses and depreciation recapture applies for this machine. 36

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38. Solution key for the previous table Col 1: simply lists the given cash flow situation, since it refers to actual cash flows, these are in then-current or future dollars Col 2 = Col 1/(1+f)Col 0 This is done to express the before-tax cash flow in today’s dollars, CVD Col 3, depreciation charges from the MACRS model. Dt = dtB; BVt = BV t-1 – Dt; dt from tables. This is measured in FD, and the asset is fully depreciated by year 6. So there is no depreciation charge in year 7 Col 4, depreciation charges in Col 3 expressed in CVD Col 5, taxable income TI in years 1—6 in CVD = CFBT-D, both expressed in CVD. i.e., Col 5= Col 2 – Col 4 . In year 7, TI = CFBT – D + DR, where the depreciation recapture comes from the fact that the salvage value in year 7 is $4655.40 (CVD) and book value is $0 (CVD). Col 6 calculates taxes as TI*0.35 Col 7 CFAT= CFBT-taxes (all in CVD) Now that we have the cash flow that we should be using which accounts for taxes/depreciation and inflation, we need to find its PW to see if it is viable. Since cashflows are in CVD, and you are given “market” MARR of 15%, you need the real interest rate i, from the expression if = i + f + i*f, which is 8.49% 38