IE 343 Midterm Exam 2 Nov 16, 2011 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. Exam 2 has three parts totally 5 problems: Part I Old problems (Difficulty: Easy), 3 old problems are selected from homework, quizzes, lecture notes Examples or textbook examples. Part II New problems (Difficulty: Median), 1 new problem. Part III Bonus (Difficulty: Hard), 1 bonus problem. Exam 2 has totally 105 Points = Part I (67 Points) + Part II (33 Points) + Part III (5 Points) You are suggested to do Part 1 first, and then part 2. Part 3 is optional. 1
Part I, 3 Problems, 67 Points: Old problems selected from homework, quizzes, lecture notes examples or textbook examples Question 1 (29 Points) Consider Projects (A D) that has the following cash flows over a study period of 5 years. We are looking for the best project to invest. The MARR is 20%, Project A Project B Project C Project D Initial Investment: $100 $300 $150 $200 Annual Revenues: $60 $90 $70 $65 Annual Expenses: $20 $15 $15 $20 Salvage Value: $20 $100 $50 $50 Useful Life: 5 Year 5 Year 5 Year 5 Year (a) Is Project A an investment alternative or cost alternative? Explain the reason why? (4 Points) (a) Investment alternative, because there s annual revenue for Project A. (b) We claim that Project D can be directly eliminated from the analysis. Why? Please explain the reason. (4 Points) (b) Project D has higher initial investment than Project C ($200 > $150), but Project D has lower net annual revenues less expenses than Project C ($45 < $55). Project C and D have the same Salvage Value $50, So Project C is a strictly better project than Project D. So Project D can be directly eliminated. 2
(c) You are calculating the IRR of the Project A. 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 project A profitable? Explain the reason why? (6 Points) (c) By linear interpolation: 25% 15% i % 15% = 9.5 15.5 0 15.5 i % = 21.2% > MARR = 20% Project A is profitable. Circle exactly one solution for part (d) to (h) (15 Points) After performing the incremental analysis procedure, we get the table below, Increment Considered (d) (e) (f) IRR 21.2% 45.0% 1.1% Is increment justified? (g) Yes No (d) Project A / Project B / Project C (the base alternative from which to begin the incremental analysis) (d) Project A (e) (B A) / (C A) / (B C) / (A C) (e) (C A) (f) (B A) / (C B) / (B C) / (A C) 3
(f) (B C) (g) Yes / No (g) Yes (h) Which Project is the best? Project A / Project B / Project C / Project D (h) Project C Question 2 (16 Points) You have two alternatives A and B with information in the table below, MARR = 10%. The salvage values at the end of useful lives of A and B are 0. A B Capital Investment 5000 7500 Annual Revenues 2000 2100 Useful Life(Years) 4 6 PW(MARR) 1340 1646 AW(MARR) 423 378 FW(MARR) at EOY 4 1962 2410 FW(MARR) at EOY 6 2373* 2916 Note: EOY stands for End of Year. PW and AW are under their own useful lives. *: Reinvest FW A at EOY 4 for two more years using MARR(10%). (i.e. FW(10%) A at EOY 6= [-5,000(F P,10%,4)+2,000(F A,10%,4)](F P,10%,2)) Useful Formulas: (A P, 10%, 4) = 0.32, (A F, 10%, 4) = 0.22, (P A, 10%, 4) = 3.17, (P F, 10%, 4) = 0.68 4
Circle exactly one solution for part (a) and (b) (8 Points) (a) If the repeatability assumption holds, which alternative will you select? (4 Points) Alternative A / Alternative B (a) Select alternative A, because AW(A) = 423 > AW(B) = 378 (b) If the study period is 6 years and the coterminated assumption holds, which alternative will you select? (4 Points) Alternative A / Alternative B (b) Select alternative B. When the coterminated assumption holds, the reinvestment rate for alternative A between year 4 and year 6 are MARR. Because FW(B) at EOY 6 = 2916 > FW(A) at EOY 6 = 2373, so select alternative B. (c) If the study period is 4 years and the imputed market value for alternative B is MV4 = 3000, which alternative will you select? Please show your calculations. (8 Points) (c) For alternative B, the cash flows become Capital Investment = 7500, Annual Revenue = 2100 for year 1-4, MV4 = 3000. PW(B) = -7500 + 2100(P/A, 10%, 4) + 3000(P/F, 10%, 4) = -7500 + 2100(3.17) + 3000(0.68) = 1197 < PW(A) = 1340 So alternative A will be selected. 5
Question 3 (22 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? (4 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... 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) Useful Formulas: (P/A,10%, 3) = 2.49; (P/A,10%, 4) = 3.17; (P/F,10%,4) = 0.68; (P/F,10%,3) = 0.75; (P/F,10%,2) = 0.83; (P/F,10%,1) = 0.91 (c) PW = -60,000 + 26,000 (P/A,10%, 3) + 18,000(P/F,10%,4) = 16980 > 0 by the Useful Formulas PW = -60,000 + 26,000 (P/A,10%, 3) + 18,000(P/F,10%,4) = 16952 > 0 by Excel So yes, I will invest this asset. 7
Part II, 1 Problems, 33 Points: New Problem Question 4 (33 Points) Same asset as in Question 3, but the asset is being depreciated under MACRS ADS method over a recovery period of three years. (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.) 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 for year 1, year 2 and year 4? (6 Points) (a) Under MACRS ADS, half-year convention is applied to year 1 and year 4. So d1 = d4 = $60,000 / 3 / 2 = $10,000, d2 = $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.... 8
(b). EOY BTCF Depr TI Tax ATCF 0 -$60,000 -$60,000 1 $30,000 $10,000 $20,000 -$8,000 $22,000 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 $10,000 $20,000 -$8,000 $22,000 (c) Are you willing to invest this asset if the income tax is considered? (6 Points) Useful Formulas: (P/A,10%, 4) = 3.17; (P/A,10%, 3) = 2.49; (P/A,10%, 2) = 1.74; (P/F,10%,4) = 0.68; (P/F,10%,3) = 0.75; (P/F,10%,2) = 0.83; (P/F,10%,1) = 0.91 (c) PW = -60,000 + 22,000(P/F,10%,1) +26,000 (P/F,10%,2) + 26,000 (P/F,10%,3) + 22,000 (P/F,10%,4) = 16060 > 0 by Useful Formulas PW = -60,000 + 22,000(P/F,10%,1) +26,000 (P/F,10%,2) + 26,000 (P/F,10%,3) + 22,000 (P/F,10%,4) = 16048 > 0 by Excel So yes, I will invest this asset. (d) If you can sell the asset at end of year 3 for $40,000, what is your capital gain (loss) on this disposal? (6 Points) (d) If the asset is sold at end of year 3, half-year convention will be applied to the depreciation deduction in year 3. d3 = $10,000 BV3 = $60,000 - $10,000 - $20,000 - $10,000 = $20,000 Capital gain (loss) = MV3 BV3 = $40,000 - $20,000 = $20,000 9
(e) If you can sell the asset at end of year 3 for $40,000, what is the tax liability (or credit) on this disposal? (3 Points) (e) Tax liability = 0.4(Capital Gain) = $20,000(0.4) = $8,000 Part III, 1 Bonus Problem, 5 Points Question 5 (5 Points) If you own the asset described in Question 3 and 4, which depreciation method would you prefer? 1) Straight Line method over a period of three years 2) MACRS ADS over a recovery period of three years 3) MACRS ADS over a recovery period of three years but sell the asset for $40,000 at the end of year 3? Explain the reason why? Show your Calculations. (You may need the table below) Useful Formulas: (P/A,10%, 4) = 3.17; (P/A,10%, 3) = 2.49; (P/A,10%, 2) = 1.74; (P/F,10%,4) = 0.68; (P/F,10%,3) = 0.75; (P/F,10%,2) = 0.83; (P/F,10%,1) = 0.91 EOY BTCF Depr TI Tax ATCF 10
We need to compare the PW of the ATCFs of these three alternatives and choose the one which maximizes the PW of the ATCFs. PW(1) = 16980 from Question 3 part(c), PW(2) = 16060 from Question 4 part(c), so we just need to calculate PW(3). EOY BTCF Depr TI Tax ATCF 0 -$60,000 -$60,000 1 $30,000 $10,000 $20,000 -$8,000 $22,000 2 $30,000 $20,000 $10,000 -$4,000 $26,000 3 $30,000 $10,000 $20,000 -$8,000 $22,000 3 $40,000 $20,000 -$8,000 $32,000 PW(3) = -60,000 + 22,000(P/F,0.1,1) +26,000(P/F,0.1,2) + (22,000+32000)(P/F,0.1,3) = - 60,000 + 22,000(0.91) + 26,000(0.83) + 54,000(0.75) = 22,100 by Useful Formulas or 22,059 by Excel. So 3) MACRS ADS over a recovery period of three years but sell the asset for $40,000 at the end of year 3 gives us higher PW than the other two alternatives. So we would prefer 3). 11
Find F given P: F = P(1 + i) N Find P given F: P = F(1 + i) N Formulas and Tables Depreciation using SL method: d k = B SV N N Depreciation using DB method: k 1 d = B(1 R) ( R) ; BV = B(1 R) k Depreciation of SL when using DB with switchover to SL: GDS depreciation: dk = rk B k Taxable Income (TI) = Gross income - all expenses (except capital investments) - depreciation deductions. k (SL) BVk SV = 1 N dk N ( k 1) [Gain (loss)on disposal] N = MV N BV N 12