CH6 Solutions

CH6 Solutions - 306-310 ENGINEERING ECONOMY SOLUTIONS TO PROBLEM SET#6 – PROJECT EVALUATION CRITERIA 1 The time distribution of cash flows

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1 3 0 6 - 3 1 0 E N G I N E E R I N G E C O N O M Y SOLUTIONS TO PROBLEM SET #6 – PROJECT EVALUATION CRITERIA 1. The time distribution of cash flows associated with the project is as follows: Time 0 : -50 000 Years 1 to 15 : 20 000 - 8000 = 12 000 To determine whether the project is worthwhile economically, the net present value may be computed, i.e., the annual cash flows are first discounted at a rate of 20 percent, the minimum acceptable return on investment, and then summed algebraically. NPV = -50 000 + 12 000 (P/A,20%,15) = -50 000 + 12 000 (4.6755) = $6106 The net present value is positive. Therefore, the project is worthwhile . 2. The cash flow profiles of the proposals are: PROPOSAL 1 Year Time 0 1 2 3 4 5 Cash Flow ($) -1500 200 400 600 800 1000 PROPOSAL 2 Year Time 0 1 2 3 4 5 Cash Flow ($) -1 500 ? 200 200 200 200 i) The rate of return (r) is the discount rate at which the net present value is zero. For pro- posal 1, we have: NPV = -1500 + [200 + 200 (A/G,r,5)] (P/A,r,5) = 0 Solving by trial and error (or with a financial calculator): At r=21%, NPV=35.92 At r=22%, NPV=-5.77 By linear interpolation, the rate of return is: 21 + [35.92 / (35.92 + 5.77)] 1% = 21.9% ii) Given that the proposals are equally acceptable at a discount rate of 14%, their net present values must be equal at that rate.
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2 Proposal 1 – NPV @ 14%: -1500 + [200 + 200 (A/G,14%,5) [ (P/A,14%,5) -1500 + [200 + 200 (1.7399) ] 3.4331 = 381 Proposal 2 – NPV @ 14%: -1500 + CF 1 (P/F,14%,1) + 200 (P/A,14%,4) (P/F,14%,1) -1500 + CF 1 (0.8772) + 200 (2.9137) (0.8772) = 0.8772 CF 1 - 989 Equating both net present values: 0.8772 CF 1 - 989 = 381 Thus, the unspecified cash flow of proposal 2 in year 1 is $1562 . 3. The time distribution of cash flows associated with the project is as follows: Time 0 : -100 000 Years 1 to 7 : 70 000 - 30 000 = 40 000 Year 8 : 70 000 - 30 000 + 20 000 = 60 000 i) Net present value: NPV = -100 000 + 40 000 (P/A,15%,7) + 60 000 (P/F,15%,8) = -100 000 + 40 000 (4.1604) + 60 000 (0.3269) = $86 030 ii) Future value equivalent: FV = -100 000 (F/P,15%,8) + 40 000 (F/A,15%,7) (F/P,15%,1) + 60 000 = -100 000 (3.0590) + 40 000 (11.0668) (1.15) + 60 000 = $263 173 or, FV = NPV (F/P,15%,8) = 86 030 (3.0590) = $263 166 Note : Discrepancies are due to round-off errors in the time value factors. iii) Equivalent annual value: EAV = -100 000 (A/P,15%,8) + 40 000 + 20 000 (A/F,15%,8) = -100 000 (0.2229) + 40 000 + 20 000 (0.0729) = $19 168 or, EAV = NPV (A/P,15%,8) = 86 030 (0.2229) = $19 176 or, EAV = FV (A/F,15%,8) = 263 173 (0.0729) = $19 185 Note : Discrepancies are due to round-off errors in the time value factors.
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3 iv) Present value ratio: PVR = NPV / 100 000 = 86 030 / 100 000 = 0.86 v) Rate of return – Determine r such that: -100 000 + 40 000 (P/A,r,7) + 60 000 (P/F,r,8) = 0 Solving by trial and error (or with a financial calculator): At r=37%, NPV=1008 At r=38%, NPV=-1220. By linear interpolation, the rate of return is:
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This note was uploaded on 10/06/2009 for the course MIME 310 taught by Professor Bilido during the Summer '08 term at McGill.

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CH6 Solutions - 306-310 ENGINEERING ECONOMY SOLUTIONS TO PROBLEM SET#6 – PROJECT EVALUATION CRITERIA 1 The time distribution of cash flows

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