UGBA 103 S
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
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
The table below gives the costs at various points in time:
Cost(t) (in $K)
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?