HW5 Soln 10

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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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## This note was uploaded on 04/09/2010 for the course ENGR ENG106 taught by Professor Hartsrough during the Winter '10 term at UC Davis.

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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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