HW5 Soln 10 - 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18...

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 ABC D E F G H I ENG106 HW#5 Winter, 2006 Problem 1 Knowns: (Read the problem statement) Two M.E. alternatives (A and B) with two years needs Constant-dollar cash flows with B-A incremental analysis as below: EOY A B B-A 0 -$30,000 -$40,000 -$10,000 1 $20,000 $43,000 $23,000 2 $18,200 $5,000 -$13,200 Find: (a) Comment on your co-worker's statement. (b) Over what range of MARR, would you recommentd the selection of machine B? Solution: (a) Whenever you need to make a rate of return comparison of M.E. alternatives, you must perform an incremental analysis. (b) Perform incremental analysis on B-A. Check if increment B-A is pure or mixed by finding an i* and then calculating PB(i*): EOY Flow PB(i*) i*: 10% =IRR(flow0:flow2) 0 -$10,000 -$10,000 1 $23,000 $12,000 =(PB at EOY 0)*(1+i*)+flow1 2 -$13,200 $0 From the project balance we see that this is a mixed investment and conclude that IRR is not equal to i*. We then compute the project balance (PB) at the end of each year as follows: PB(IRR, MARR) 0 = -$10, 000 PB(IRR, MARR) 1 = -$10, 000(1+IRR) + $23,000 = $13,000 - $10,000 IRR PB(IRR, MARR) 2 = ($13, 000 - $10,000 IRR)(1+MARR) - $13,200 = $0 Rearranging terms in PB(IRR, MARR) 2 gives an expression for IRR as a function of MARR: IRR = 1.3 -1.32 / (1+MARR) This is plotted in Fig. 1, from which we conclude that project B will be accepted if 10%<MARR<20% which is the range over which IRR for B-A >MARR Figure 1. IRR vs. MARR 6% 8% 10% 12% 14% 16% 18% 20% 22% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24% MARR IRR IRR MARR
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55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 ABC D E F G H I Problem 2 Knowns: (Read the problem statement) Cash flow shown in the Table below: Find: (a) Use IRR function (which is really an i* function) to find all i* in the range EOP Flow 0% to 50%. 0 -$150 (b) Plot PW of the cash flow, for MARR 1 $100 in the range 0% to 50%. 2 $200 (c)
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HW5 Soln 10 - 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18...

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