IE 343 Midterm Exam 2 April 6, 2012 Version A Closed book, closed notes. 50 minutes Write your printed name in the spaces provided above on every page. Show all of your work in the spaces provided. Interest rate tables are provided for you to use in questions that require numerical answers. Exam 2 has three Parts totally 5 Problems with 105 Points: Part I 3 Old Problems, totally 76 Points. The old problems are selected from Homework, Quizzes, Lecture Notes Examples and Textbook Examples with numbers changed. Part II 1 New Problem, 24 Points. Part III 1 Bonus Problem, 5 Points. You are suggested to do Part I first, and then part II. Part III is optional. Version A 1
Part I 3 Old Problems, totally 76 Points: old problems selected from Homework, Quizzes, Lecture Notes Examples or Textbook Examples Question 1 (35 Points) We consider four design alternatives D1, D2, D3, D4 each with a useful life of 5 years. The MARR is 20%. D1 D2 D3 D4 Initial Investment: $100 $300 $150 $200 Annual Revenues: $50 $90 $70 $65 Annual Expenses: $20 $15 $15 $20 Salvage Value: $30 $100 $50 $50 Useful Life: 5 Year 5 Year 5 Year 5 Year (a) Are the four design alternatives D1, D2, D3, D4 investment alternatives or cost alternatives? Please explain why? (3 Points) (a) Investment alternative, because there are annual revenues. (b) We claim that the design alternative D4 can be directly eliminated from the analysis. Why? Please explain the reason. (4 Points) (b) D4 has higher initial investment than D3 ($200 > $150), but D4 has lower net annual revenues less expenses than D3 ($45 < $55). D3 and D4 have the same Salvage Value $50, So D3 is a strictly better alternative than D4. So D4 can be directly eliminated. Version A 2
(c) You are calculating the IRR of D1. You get PW(15%) = 15.5, and PW(25%) = -9.5 by trial and error. What is the approximated IRR using linear interpolation? Based on this approximated IRR, is D1 profitable? Explain the reason why? (8 Points) (c) By linear interpolation: D1 is profitable. Circle exactly one solution for part (d) to (h) (20 Points) After eliminating D4, we can perform the incremental analysis procedure using IRR. The table we get is as follows, Increment Considered (D1 DN) (d) (f) Capital Investment $100 $50 $150 Annual Revenues Less Expenses $30 $25 $20 Salvage Value $30 $20 $50 Useful life(years) 5 5 5 IRR 21.2% 45.01% 0.00% Is increment justified by IRR? Yes Yes No Which alternative will you select? D1 (e) (g) (d) (D1 D3) / (D2 D3) / (D3 DN) / (D3 D1) (d) (D3 D1) (e) D1 / D2 / D3 / DN (e) D3 Version A 3
(f) (D2 D3) / (D3 D2) / (D3 DN) / (D3 D1) (f) (D2 D3) (g) D1 / D2 / D3 / DN (g) D3 (h) Which design alternative is the best? D1 / D2 / D3 / D4 (h) D3 Question 2 (20 Points) Two mutually exclusive alternatives are being considered for the environmental protection equipment at a petroleum refinery. One of these alternatives must be selected. The estimated case flows for each alternative are follows: Alternative A Alternative B Capital investment $6,000 $5,000 Annual expenses $2,000 $2,500 Salvage value at end of useful life $1,000 $500 Useful life 4 years 8 years Version A 4
(a) Which environmental protection equipment alternative should be selected? The firm s MARR is 10% per year. Assume the equipment will be needed indefinitely. (10 Points) (a) Since the equipment will be needed indefinitely, the repeatability assumption holds. AW(A) = -6000(A/P,0.1,4)-2000+1000(A/F,0.1,4) = -6000*0.3155-2000+1000*0.2155 = -3677.5 AW(B) = -5000(A/P,0.1,8)-2500+500(A/F,0.1,8) = -5000*0.1874-2500+500*0.0874 = -3393.3 Select Alternative B, since AW(B) = -3393.3 > AW(A) = -3677.5 (b) Assume the study period is shortened to four years. The firm s MARR is 10% per year. The market value of Alternative B at the end of year four is estimated to be $3,000. Use the imputed market value technique to determine which alternative you would recommend. (10 Points) (b) AW(A) = -3677.5 AW(B) = -5000(A/P,0.1,4)-2500+3000(A/F,0.1,4) = -5000*0.3155-2500+3000*0.2155 = -3431 Select Alternative B, since AW(B) = -3431 > AW(A) = -3677.5 Version A 5
Question 3 (21 Points) Suppose that an asset with a cost basis of $60,000 is expected to produce net revenues of $30,000 per year during the four year period, and its terminal market value is negligible. The effective income tax rate is 40% and the after-tax MARR is 10% per year. The asset is being depreciated under the Straight Line method over a period of three years. EOY (A) BTCF (B) Depreciation (C)=(A) (B) Taxable Income (D)= t(c) Income Taxes (E)=(A)+(D) ATCF (a) What is the depreciation deduction d2 for year 2? (3 Points) (a) Since Straight Line method is applied, the depreciation deduction is the same every year, d2 = d = $60,000 / 3 = $20,000 (b) Complete the table below with information given above. (12 Points) EOY BTCF Depr TI Tax ATCF 0 -$60,000 -$60,000 1 $30,000.... 2 $30,000.... 3 $30,000.... 4 $30,000... Version A 6
(b). EOY BTCF Depr TI Tax ATCF 0 -$60,000 -$60,000 1 $30,000 $20,000 $10,000 -$4,000 $26,000 2 $30,000 $20,000 $10,000 -$4,000 $26,000 3 $30,000 $20,000 $10,000 -$4,000 $26,000 4 $30,000 $30,000 -$12,000 $18,000 (c) Are you willing to invest this asset if the income tax is considered? (6 Points) (c) PW = -60,000 + 26,000 (P/A,10%, 3) + 18,000(P/F,10%,4) = -60,000 + 26,000*2.4869 + 18,000*0.6830 = 16,953 > 0 So I will invest this asset. Version A 7
Part II, 1 Problem, 24 Points: New Problem Question 4 (24 Points) XYZ Corp. is considering buying a computer workstation for $1,000. The equipment is in the 3-year MACRS (GDS) property class and is expected to reduce net operating expenses by $500 every year. The company s effective income tax rate is 40%. Assume that the after-tax MARR is 10% per year and the study period is 4 years. EOY (A) BTCF (B) Depreciation (C)=(A) (B) Taxable Income (D)= t(c) Income Taxes (E)=(A)+(D) ATCF (a) What are the depreciation deductions d2 and d3 for year 2 and 3? (4 Points) EOY BTCF Depr 0 -$1,000 1 $500 d1 = $333.3 2 $500 d2 =. 3 $500 d3 =. 4 $500 d4 = $74.1 (a) Under 3-year MACRS GDS r1 = 0.3333, r2 = 0.4445, r3 = 0.1481, r4 = 0.0741 EOY BTCF Depr 0 -$1,000 1 $500 d1 = $333.3 2 $500 d2 = $444.5. 3 $500 d3 = $148.1. 4 $500 d4 = $74.1 Version A 8
(b) If you can sell the asset at end of year 2 for $500, what is your capital gain (loss) on this disposal? What is the tax liability (or tax credit) on this disposal? (10 Points) (b) If the asset is sold at end of year 2, half-year convention will be applied to the depreciation deduction in year 2. Now d2 = $444.5/2 = $222.25 BV 2 = $1,000 - $333.3 - $222.25 = $444.45 Capital gain (loss) = MV 2 BV 2 = $500 - $444.45 = $55.55 Tax liability = 0.4(Capital gain) = 0.4 ($55.55) = $22.22 (c) If you can sell the asset at the end of year 2 for $500, please complete the table below. (10 Points) EOY BTCF Depr TI Tax ATCF 0 -$1,000 -$1,000 1 $500.... 2 $500.... 2 $500... (c). EOY BTCF Depr TI Tax ATCF 0 -$1,000 -$1,000 1 $500 $333.3 $166.7 -$66.68 $433.32 2 $500 $222.25 $277.75 -$110.1 $388.9 2 $500 $55.55 -$22.22 $477.78 Version A 9
Part III, 1 Bonus Problem, 5 Points Question 5 Extension of Question 4 (5 Points) XYZ Corp. is considering buying a computer workstation for $1,000. The equipment is in the 5-year MACRS (ADS) property class and is expected to reduce net operating expenses by $500 every year. The company s effective income tax rate is 40%. Assume that the after-tax MARR is 10% per year and the study period is 4 years. The market value of the computer workstation at the end of year 4 is considered to be negligible. Please complete the table below. EOY BTCF Depr TI Tax ATCF 0 -$1,000 -$1,000 1 $500.... 2 $500.... 3 $500.... 4 $500.... 4 $0... For 5-year MACRS (ADS) property class, we need 6 years to fully depreciate the computer workstation. Study period is 4 years and the market value of the computer workstation is negligible after 4 years, which means there s an early disposal in year 4. Then half year convention should be applied to the 4 th year. For MACRS (ADS), straight line method with half year convention to the 1 st year is applied, so d1=1000/5/2=100, d2=d3=1000/5=200, d4=1000/5/2=100 BV4 = 1000-d1-d2-d3-d4 = 1000-100-200-200-100 = 400 MV4 = 0 Capital gain (loss) = MV4 BV4 = 0 400 = -400 Tax credit = -0.4 * (-400) = 160 Version A 10
EOY BTCF Depr TI Tax ATCF 0 -$1,000 -$1,000 1 $500 $100 $400 -$160 $340 2 $500 $200 $300 -$120 $380 3 $500 $200 $300 -$120 $380 4 $500 $100 $400 -$160 $340 4 $0 -$400 $160 $160 Version A 11
Find F given P: Find P given F: Imputed Market Value: Formulas and Tables Capital Investment, : Salvage Value, : Useful life, : Study Period Depreciation using SL method: ; Depreciation using DB method: ; ; Depreciation of SL when using DB with switchover to SL: GDS or ADS depreciation: dk rk B Taxable Income (TI) = Gross income - all expenses (except capital investments) - depreciation deductions. [Gain(loss)on disposal] N MV N BV N Version A 12
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