1.

Suppose a firm with a cost of capital of 8% per year needs equipment

on an ongoing basis. The equipment costs $700,000 to buy at t=0, and the

operating and maintenance (O&M) costs at t=1,2,3,4 are $250,000,

$300,000, $400,000, and $600,000 respectively. Work out how often the

firm should replace one unit with another in order to minimize the total costs

(sum of replacement and O&M costs).

2.

ABC Fitness Club has a set of treadmills and other exercise

equipment that costs $600,000. They replace the entire set every 300 weeks

with an identical set, and sell the old set for $60,000. 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 50 weeks

ago. Therefore, given the replacement policy and normal use, it will be

replaced in exactly 250 weeks 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 225 weeks if they still want to sell it for $60,000. In other

words, the life of the current set of equipment that ABC has will be

shortened by 25 weeks on account of its use by members of XYZ Health

Club. Assuming the discount rate to be 0.18% per week, what payment from

XYZ Health Club would compensate ABC Fitness Club for the fact that

their current equipment will need replacement 25 weeks earlier?