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Solution to 2009 Midterm

# Solution to 2009 Midterm - NAME HAAS SCHOOL OF BUSINESS...

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N AME : H AAS S CHOOL OF B USINESS U NIVERSITY OF C ALIFORNIA AT B ERKELEY UGBA 103 T AKE -H OME M ID - TERM E XAMINATION J ULY 23, 2009 TO J ULY 27, 2009 D UE IN THE B OX O UTSIDE F494 AT 9 AM ON J ULY 27, 2009 S HOW WORK FOR PARTIAL CREDIT . E ACH Q UESTION HAS 12.5 POINTS . 1. Suppose you have to decide between two machines that have the following cash flows in millions of dollars: Machine Life (in years) C 0 C 1 C 2 C 3 C 4 C 5 A 3 –15 9 8 9 B 5 –15 6 6 6 6 6 Given a discount rate of 12% per year, work out the NPV (Net Present Value) of each machine, and state which machine is more attractive financially (a) without future replacement, and (b) with future replacement. (a): As the table below shows, machine B has a higher NPV. Given: Discount rate 12% Time (t) 0 1 2 3 4 5 NPV 0 DF t 1 0.8929 0.7972 0.7118 0.6355 0.5674 CF A -15 9 8 9 PV(CF A ) -15 8.04 6.38 6.41 5.82 CF B -15 6 6 6 6 6 PV(CF B ) -15 5.36 4.78 4.27 3.81 3.40 6.63 (b): As the table below shows, machine A has a higher EAF. Given: Discount rate 12% Time (t) 0 1 2 3 4 5 NPV 0 Life (n) AF (12%,n) EAF DF t 1 0.8929 0.7972 0.7118 0.6355 0.5674 CF A -15 9 8 9 3 PV(CF A ) -15 8.04 6.38 6.41 5.82 2.40 2.42 CF B -15 6 6 6 6 6 5 PV(CF B ) -15 5.36 4.78 4.27 3.81 3.40 6.63 3.60 1.84

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H AAS S CHOOL OF B USINESS U NIVERSITY OF C ALIFORNIA AT B ERKELEY UGBA 103 A VINASH V ERMA Name: 2. Suppose you are given that an equipment costs \$150,000 to buy at t=0, and the operating and maintenance (O&M) costs at t =1,2,…8 are \$25,000, \$30,000, \$45,000, \$45,000, \$60,000, \$60,000, \$90,000, and \$100,000 respectively. The equipment is needed on an ongoing basis, and you are asked to decide how often we should replace one unit with another in order to minimize the total costs (sum of replacement and O&M costs). In other words, you are asked to work out the economic life of the equipment. Assume that the discount rate is 16% per year. Given: Discount rate 16.0% Time (t) 0 1 2 3 4 5 6 7 8 DF t 1 0.8621 0.7432 0.6407 0.5523 0.4761 0.4104 0.3538 0.3050 Costs 150 25 30 45 45 60 60 90 100 PV 0 (Costs) 150 21.552 22.295 28.83 24.853 28.5668 24.63 31.8447 30.502546 Cumulative PV 0 (Costs) 171.55 193.85 222.68 247.53 276.096 300.7 332.567 363.06983 AF(20%, t) 0.8621 1.6052 2.2459 2.7982 3.2743 3.6847 4.0386 4.3436 EAC t 199 120.76 99.148 88.461 84.3223 81.61 82.3479 83.587482 The table above works out the EAC and shows that it is lowest for 6 years. ALTERNATIVE : The answer above is confirmed by the table below, which works out the present value of the perpetuity of costs for each replacement policy: Time (t) 0 1 2 3 4 5 6 7 8 Costs 150 25 30 45 45 60 60 90 100 DF t 1 0.8621 0.7432 0.6407 0.5523 0.47611 0.41 0.35383 0.3050255 PV 0 (Costs) 150 21.552 22.295 28.83 24.853 28.5668 24.63 31.8447 30.502546 Cumulative PV 0 (Costs) 171.55 193.85 222.68 247.53 276.096 300.7 332.567 363.06983 t-yearly Discount rate 16% 35% 56% 81% 110% 144% 183% 228% PV -t of the Perpetuity 1072.2 560.9 397 305.35 250.919 209.4 182.107 159.35194 PV 0 of the Perpetuity 1243.8 754.75 619.68 552.88 527.015 510.1 514.674 522.42176 The t-year discount rate is worked out as r tyr = 1.16 t –1. Thus, r 2yr = 1.16 2 –1 = 1.3456 –1 = 34.56%; r 3yr = 1.16 3 –1 = 1.560896 –1 = 56.0896%; and so on. Solution to Summer 2009 Take-Home Mid-term Examination 2
H AAS S CHOOL OF B USINESS U NIVERSITY OF C ALIFORNIA AT B ERKELEY UGBA 103 A VINASH V ERMA Name: 3. ABC Fitness Club has a set of treadmills and other exercise equipment that costs \$225,000. They replace the entire set every 72 months with an identical set, and sell the old set for \$45,000. The technology and the prices are expected to remain unchanged in perpetuity. Therefore, as a going concern, ABC Fitness Club can be reasonably expected to follow this replacement policy for ever. They bought the current equipment 15 months ago. Therefore, given the replacement policy and normal use, it will be replaced in exactly 57 months from now.

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Solution to 2009 Midterm - NAME HAAS SCHOOL OF BUSINESS...

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