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# PS5Answers - Problem 1 Part 1 NPV Year 0 1 2 3 4 Machine A...

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Problem 1) Part 1 Machine A PV Machine B PV NPV \$61.42 \$61.42 \$49.21 \$49.21 The calculation in the C/E-columns uses the Year 0 -80.00 -80.00 -100.00 -100.00 EXCEL NPV-function (careful, you need 1 50.00 45.45 60.00 54.55 to multiply by 1.1 in order to correct for 2 50.00 41.32 60.00 49.59 the fact that the function assumes payments 3 50.00 37.57 60.00 45.08 run from year 1-5 rather than 0-4!!). 4 25.00 17.08 All Numbers are in Thousands However, since the machines will need to be replaced and have different lives Machine A Machine B NPV \$61.42 \$49.21 \$19.38 \$19.79 Use EXCEL \$19.38 \$19.79 The last line uses the EXCEL PMT function to compute the equivalent annual cash flow. Machine B is the better choice. To see this another way, we could look at a 12 year period: Over 12 years, we would go through three new Machine As, or four new Machine Bs With Machine A, we get 25 in year 4 and 8, but pay out 80. With Machine B, we get \$60 and pay \$100 in years 3, 6 and 9 These "projects" have the same life, and can be compared directly. As seen above, Machine B is the better choice. Machine A PV Machine B PV NPV 132.02 132.02 134.83 134.83 Year 0 -80.00 -80.00 -100.00 -100.00 1 50.00 45.45 19.38 60.00 54.55 19.79 2 50.00 41.32 19.38 60.00 49.59 19.79 3 50.00 37.57 19.38 -40.00 -30.05 19.79 4 -55.00 -37.57 19.38 60.00 40.98 19.79 5 50.00 31.05 19.38 60.00 37.26 19.79 6 50.00 28.22 19.38 -40.00 -22.58 19.79 7 50.00 25.66 19.38 60.00 30.79 19.79 8 -55.00 -25.66 19.38 60.00 27.99 19.79 9 50.00 21.20 19.38 -40.00 -16.96 19.79 10 50.00 19.28 19.38 60.00 23.13 19.79 11 50.00 17.52 19.38 60.00 21.03 19.79 12 25.00 7.97 19.38 60.00 19.12 19.79 Part 2 In order to use Machine B, there is a one time cost of \$10,000 for retooling. We can view the Annual Equivalent as a perpetuity, since we will buy new machines as the old ones wear out. Consider the values we already calculated, without considering the \$10,000 cost Machine A Machine B Difference 19.38 19.79 0.41 193.76 197.89 4.13 Since the value of going with Machine B is only \$4,130 more than the value of Machine A, Machine A has an NPV of 61.42 while Machine B has an NPV of 49.21 more work must be done. We need to calculate the annual equivalent. Annual Equivalent Present value of equivalent Cash flow Present value of equivalent Cash flow Annual Equivalent Value of Perpetuity

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it will not be worth buying Machine B if we have to pay \$10,000 to retool the factory. Part 3 The old machine should be replaced when its annual cashflow falls below the annual equivalent of the replacement. Replace? Year 1 50.00 19.79 No Year 2 20.00 19.79 No Year 3 0.00 19.79 Yes Part 4 The 12 year argument in Part 1 shows that Machine B should be chosen when the time period is only 24 years. Note that the Annual equivalent method will also work, but the formula for an annuity should be used rather than the formula for a perpetuity. This gives: Machine A \$174.08 Machine B \$177.79 Difference (B-A) \$3.71 Hence, if both machines have to be used for another 24 years, using machine B gives a higher NPV Note that the one-time re-tooling fee will lead, as in part 2, to the choice of machine A as the optimal decision. This follows from the fact that the NPV of machine B will fall to \$167,790 which is lower than the NPV of machine A. Old Machine A.E. Machine B of \$3,710.
Problem 2) step 1 - determine the cashflows: Net income: 11,000.

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PS5Answers - Problem 1 Part 1 NPV Year 0 1 2 3 4 Machine A...

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