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Unformatted text preview: N AME : KEY H AAS S CHOOL OF B USINESS U NIVERSITY OF C ALIFORNIA AT B ERKELEY BA 103 S UMMER 2007 T AKEH OME M ID TERM E XAMINATION J UNE 8, 2007 TO J UNE 12, 2007 S HOW WORK FOR PARTIAL CREDIT . 1. ABC Fitness Club has exercise equipment that costs $135,000. They replace it every six years with an identical unit [the same make and model], and sell the old unit 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. In June 2005, exactly two years ago, they bought the current equipment. Therefore, given the replacement policy and normal use, it will be replaced in exactly four years from now. XYZ Health Club, a sister facility in the neighborhood, closed down temporarily, and asked ABC Fitness Club to let its members use ABCs 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 forty months if they still want to sell the old unit for $45,000. In other words, the life of the current unit will be shortened by eight months on account of its use by members of XYZ Health Club. Assuming the discount rate to be 0.75% per month, what payment from XYZ Health Club would compensate ABC Fitness Club for the fact that their current equipment will need replacement 8 months earlier? 20 points A LTERNATIVE 1 (U SING P ERPETUITY V ALUATION F ORMULA ): With normal use, when the equipment is replaced in 4 years (in 48 months, or at t=48), there will be a net cash outflow of $90000 (Outflow of $135000 and Inflow of $45000). After that, net cash outflows of $90000 will occur every 72 months in perpetuity. Thus the normal use stream has cash flows of $90K at t=48,120,192,, and so on ad infinitum . The frequency of cash flows is 72 months, which means we need the 72 monthly rate, which works out to be (1.0075) 72 1 = 71.25527%. Using the perpetuity valuation formula C / r = $90,000/0.7125527 = $126,306.45 gives us the value at t=24, which is one 72 month period before t=48, when the first cash flow in perpetuity occurs. Bringing, PV 24 (Normal use perpetuity) = $126,306.45 forward 24 months in time, we get: PV (normal use perpetuity) = $126,306.45*(1.0075) 24 = $151,114.74. With excessive use, the equipment will be replaced in 40 months, or at t=40, occasioning a net cash outflow of $90000. After that, net cash outflows of $90000 will occur every 72 months in perpetuity. Thus the excessive use stream has cash flows of $90K at t=40,112,184,, and so on ad infinitum . The frequency of cash flows is 72 months, and using the perpetuity valuation formula C / r = $90,000/0.7125527 = $126,306.45 gives us the value at t=32, which is one 72month period before t=40, when the first cash flow in perpetuity occurs. Bringing, PV 32 (Excessive use perpetuity) = $126,306.45 forward 32 months in time, we get: PVperpetuity) = $126,306....
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 Spring '08
 MCCULLOUGH

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