Solution to 2008 Midterm

Solution to 2008 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 S UMMER 2008 S OLUTION TO T AKE -H OME M ID - TERM E XAMINATION J UNE 13, 2008 TO J UNE 18, 2008 D UE IN MY MAILBOX IN R OOM F578 AT 3.30 PM S HOW WORK FOR PARTIAL CREDIT . 1. Suppose we are given that an equipment costs $144,000 to buy at t=0, and the operating and maintenance (O&M) costs at t =1,2,…8 are $10,000, $15,000, $20,000, $25,000, $35,000, $50,000, $70,000, and $95,000 respectively. The equipment is needed on an ongoing basis, and the firm has to decide how often it should replace one unit with another in order to minimize the total costs (sum of replacement and O&M costs). In other words, the firm needs to work out the economic life of the equipment. Assume that the discount rate is 4.5%, and work out how often it is that the firm should replace the equipment so as to minimize the total costs (sum of 20 points The table below gives the costs at various points in time: t DF t Cost(t) (in $K) PV 0 (Costs) NPV t AF(4.5%, t) EAC t 0 1 144 144 1 0.9569 10 9.5694 153.5694 0.9569 160.48 2 0.9157 15 13.7359 167.3054 1.8727 89.3406 3 0.8763 20 17.5259 184.8313 2.7490 67.2367 4 0.8386 25 20.9640 205.7953 3.5875 57.3641 5 0.8025 35 28.08579 233.8811 4.3900 53.2762 6 0.7679 50 38.3948 272.2759 5.1579 52.7884 7 0.7348 70 51.4380 323.7139 5.8927 54.9347 8 0.7032 95 66.8026 390.5164 6.5959 59.2061 The economic life is 6 years. 2. ABC Fitness Club has exercise equipment that costs $234,000. They replace it every 20 quarters with an identical unit [the same make and model], and sell the old unit for $54,000. 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 5 quarters ago. Therefore, given the replacement policy and normal use, it will be replaced in exactly 15 quarters from now. XYZ Health Club, a sister facility in the neighborhood, closed down temporarily, and asked ABC Fitness Club to let its members use ABC’s facilities until it reopens. Taking into account the membership of the two clubs, it is estimated that ABC Club will have to replace their current equipment in 12 quarters if they still want to sell the old unit for $54,000. In other words, the life of the current unit will be shortened by 3 quarters on account of its use by members of XYZ Health Club. Assuming the discount rate to be 3.15% per quarter, what payment from XYZ Health Club would compensate ABC Fitness Club for the fact that their current equipment will need replacement 3 quarters earlier? 20 points
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Solution to 2008 Midterm - NAME: HAAS SCHOOL OF BUSINESS...

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