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ENGM 661 Engineering Economics

ENGM 661 Engineering Economics. Depreciation & Taxes. Today’s learning objectives:. Given an initial Price, class life, and end of useful life salvage value, be able to compute a depreciation schedule for straight line depreciation decline balance method (100% < p < 200%)

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ENGM 661 Engineering Economics

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  1. ENGM 661 Engineering Economics Depreciation & Taxes

  2. Today’s learning objectives: • Given an initial Price, class life, and end of useful life salvage value, be able to compute a depreciation schedule for • straight line depreciation • decline balance method (100% < p < 200%) • declining balance with automatic conversion to straight line • declining balance with conversion to straight line using the half-year convention • MACRS depreciation • Be able to compute a depletion schedule using adjusted cost basis. Given an estimated Net Income, be able to compute a corporate income tax. Given a before tax cash flow, be able to compute an after tax cash flow.

  3. U.S. income tax rates have changed significantly over the past 100 years. Shown below are the top marginal income tax rates for individuals and corporations. Source: www.taxpolicycenter.org for top individual tax rates and top corporate rates.

  4. Corporate Tax Rate

  5. Performing Income Tax Calculations Can Be Challenging Congress Has Simplified Income Tax Calculations for 2012

  6. Example 10.1 A small business is forecasting a taxable income of $50,000 for the year. The owner is considering making an investment that will increase taxable income by $45,000. If the investment is pursued and the anticipated return occurs, what will be the magnitude of the increase in income taxes caused by the new investment? What would be the magnitude of the increase in income taxes if the company forecasts a taxable income of $400,000 for the year?

  7. Example 10.1 With a “base” taxable income of $50,000, the federal income tax will be 0.15($50,000), or $7500. The income tax for a taxable income of $95,000 will be $13,750 + 0.34($20,000) = $20,550. With a “base” taxable income of $400,000, the federal income tax will be $113,900 + 0.34($65,000) = $136,000 or 34% of $400,000. Because every dollar of the additional $45,000 in taxable income will be taxed at 34%, the increase in taxable income will be 0.34($45,000) = $15,300 for a total tax of $151,300.

  8. effective tax rate= income tax divided by taxable income; • incremental tax rate= average rate charged to incremental taxable income; and • marginal tax rate= tax rate that applies to the last dollar included in taxable income.

  9. Example 10.2 For Example 10.1, the effective tax rate, when “base” taxable income is $50,000 and an additional $45,000 in taxable income will occur, is $20,550/($50,000 + $45,000), or 21.63%. The incremental tax rateis ($20,550 - $7500)/$45,000, or 29%. The marginal tax rateis 34%.

  10. Effective tax rates vary significantly among corporations, as shown below for FY 2010. Favorable tax rates in and tax incentives provided by developing countries contribute significantly to reduced effective tax rates.

  11. Sole Proprietor vs S-Corp Savings = $4590* *less corporate tax

  12. Taxable Income + Gross Income - Depreciation Allowance - Interest on Borrowed Money - Other Tax Exemptions = Taxable Income

  13. Corporate Tax Ex: Suppose K-Corp earns $5,000,000 in revenue above manufacturing and operations cost. Suppose further that depreciation costs total $800,000 and interest paid on short and long term debt totals $1,500,000. Compute the tax paid.

  14. Corporate Tax Gross Income $ 5,000,000 Depreciation - 800,000 Interest - 1,500,000 Taxable Income $ 2,700,000

  15. Corporate Tax Gross Income $ 5,000,000 Depreciation - 800,000 Interest - 1,500,000 Taxable Income $ 2,700,000 Tax = $ 113,900 + .34(2,700,000 - 335,000) = $936,400

  16. After Tax Cash Flow + Gross Income - Interest = Before Tax Cash Flow

  17. After Tax Cash Flow + Gross Income - Interest = Before Tax Cash Flow - Tax = After Tax Cash Flow

  18. After Tax Cash Flow Ex: Suppose K-Corp earns $5,000,000 in revenue above manufacturing and operations cost. Suppose further that depreciation costs total $800,000 and interest paid on short and long term debt totals $1,500,000. Compute the after tax cash flow.

  19. After Tax Cash Flow Gross Income $ 5,000,000 Depreciation - 800,000 Interest - 1,500,000 Before Tax Cash Flow $ 2,700,000

  20. After Tax Cash Flow Gross Income $ 5,000,000 Interest - 1,500,000 Before Tax Cash Flow $3,500,000 Less Tax $936,400 After Tax Cash Flow $2,563,600

  21. Methods of Depreciation • Straight Line (SL) • Sum-of-Years Digits (SYD) • Declining Balance (DB) • Prior to 1981 • Accelerated Cost Recovery System (ACRS) • 1981-86 • Modified Accelerated Cost Recovery (MACRS) • 1986 on

  22. Straight Line (SLD) Let P = Initial Cost n = Useful Life s = Salvage Value year n Dt = Depreciation Allowance in year t Bt = Unrecovered Investment (Book Value) in year t Then Dt = (P - S) / n Bt = P - [ (P - S) / n ]t

  23. Ex: Straight Line Depr. Let P = $100,000 n = 5 years s = $ 20,000 Then Dt = (P - S) / n = $ 16,000 B5 = P - [ (P - S) / n ] 5 = $ 20,000

  24. Declining Balance In declining balance, we write off a constant % , p, of remaining book value D1 = pP , P = initial cost ‘p= factor/n normally 2/n or 1.25/n or 1.5/n B1 = P - D1 = P - pP = P(1-p) D2 = pB1 = pP(1-p)

  25. Declining Balance In declining balance, we write off a constant % , p, of remaining book value B2 = B1 - D2 = P(1-p) - pB1

  26. Declining Balance In declining balance, we write off a constant % , p, of remaining book value B2 = B1 - D2 = P(1-p) - pB1 = P(1-p) - pP(1-p)

  27. Declining Balance In declining balance, we write off a constant % , p, of remaining book value B2 = B1 - D2 = P(1-p) - pB1 = P(1-p) - pP(1-p) = P(1-p)[1 - p]

  28. Declining Balance In declining balance, we write off a constant % , p, of remaining book value B2 = B1 - D2 = P(1-p) - pB1 = P(1-p) - pP(1-p) = P(1-p)[1 - p] = P(1-p)2

  29. Declining Balance In declining balance, we write off a constant % , p, of remaining book value B2 = B1 - D2 = P(1-p) - pB1 = P(1-p) - pP(1-p) = P(1-p)2 Dt = p [ P (1 - p) t - 1] Bt = P (1 - p) t

  30. Ex: Declining Balance P = $100,000 n = 5 years S = $20,000 p = 2/5 (200% declining balance) Then D1 = (2/5)(100,000) = $40,000 D5 = ? , B5 = ?

  31. Ex: Declining Balance P = $100,000 n = 5 years S = $20,000 p = 2/5 (200% declining balance) Then D1 = (2/5)(100,000) = $40,000 B1 = 100,000 - 40,000 = $ 60,000 D5 = ? , B5 = ?

  32. Ex: Declining Balance P = $100,000 n = 5 years S = $20,000 p = 2/5 (200% declining balance) Then D1 = (2/5)(100,000) = $ 40,000 B1 = 100,000 - 40,000 = $ 60,000 D2 = (2/5)(60,000) = $ 24,000 D5 = ? , B5 = ?

  33. Ex: Declining Balance (cont) • Dt = p [ P (1 - p) t - 1] • D5 = .4(100,000)(.6) 4 • = $ 5,184 • Bt = P (1 - p) t • B5 = 100,000(.6) 5 • = $ 7,776

  34. Ex: Declining Balance (cont) • Dt = p [ P (1 - p) t - 1] • D5 = .4(100,000)(.6) 4 • = $ 5,184 • Bt = P (1 - p) t • B5 = 100,000(.6) 5 • = $ 7,776 Note that Declining Balance will never depreciate book value to $0. It will, however, depreciate past the salvage value

  35. Time Value of Tax Savings(Tax Rate = 40%)

  36. Double Declining Converting to SL½ year convention • MACRS are built off of this • Pick the Maximum Depreciation between Straightline Depreciation & Declining Balance. • Year 1 SL = (Book Value/n)*.5 • Year 1 Declining balance = P/2*Book Value • Year 1 Depreciation = Max Depreciation of SL and Declining Balance • Year 2-Year N-1 SL Depreciation= Book Valuet-1 /(n-t+.5) • Year 2 - Year N-1 Declining Balance Depreciation= Book Valuet-1*P

  37. DDB/SL Conversion(Salvage = $0)

  38. DDB/SL Conversion(Salvage = $0)

  39. DDB/SL Conversion(Salvage = $0)

  40. DDB/SL Conversion(Salvage = $0)

  41. DDB/SL Conversion(Salvage = $0)

  42. Class Problem Ex: Suppose K-Corp is interested in purchasing a new conveyor system. The cost of the conveyor is $180,000 and may be depreciated over a 5 year period. K-Corp uses 150% declining balance method with a conversion to straight line. Compute the depreciation schedule over the 5 year period.

  43. Class Problem

  44. Class Problem (p = 1.5/5 = .3)

  45. Class Problem

  46. DDB/SL Conversion(Half-Year Convention)

  47. DDB/SL Conversion(Half-Year Convention)

  48. DDB/SL Conversion(Half-Year Convention)

  49. Class Problem A $180,000 piece of machinery is installed and is to be depreciated over 5 years. You may assume that the salvage value at the end of 5 years is $ 0. The method of depreciation is to be double declining balance with conversion to straight line using the half-year convention (you may only deduct 1/2 year of depreciation in year 1). Establish a table showing the depreciation and the end of year book value for each year.

  50. Class Problem

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