Digital Convert (DC) is a three- year- old start- up company with most of its capital coming from banks and personal investments by the founders. DC manufactures a high- resolution scanner (MXP35). At the heart of the MXP35 is a photoelectric light sensor that converts light into digital pixels. DC currently produces the MXP35 for $ 480 (variable cost) per unit and incurs virtually no fixed manufacturing costs. All of its equipment is leased, and the leases are structured whereby DC only pays for the actual units produced. DC operates out of a building that is provided free by New York State for entrepreneurial start- ups. New York State also pays utilities, taxes, insurance, and administrative costs. DC does have fixed financing costs to service its existing loans, and these financing costs consume most of its profits from sales of the MXP35. DC faces the following monthly demand schedule for the MXP35 (where price is the wholesale price DC receives):

Quantity Price
19 ........... $ 1,278
20 ........... 1,240
21 ........... 1,202
22 ........... 1,164
23 ........... 1,126
24 ........... 1,088
25 ........... 1,050
26 ........... 1,012

(The equation of the demand curve for the above table is: P = $ 2,000 – 38 Q). In other words, if DC wants to sell 20 MXP35s per month, it would charge a wholesale price of $ 1,240 per unit.

a. Given DC’s current cost structure of $ 480 variable cost and zero fixed costs, what is its profit- maximizing price- quantity combination for MXP35?
b. DC learns of a new manufacturing process for their photoelectric light sensor that lowers the variable cost from $ 480 per unit to $ 100 per unit. But the equipment must be leased for $ 7,000 per month for 24 months. If DC leases the new equipment, then over the next 24 months DC commits to paying $ 7,000 each month. If DC installs the new equipment, what is the price- quantity combination that maximizes profits? (Assume the quality and quantity of sensors produced by the existing and new technologies are identical.)
c. Before deciding to adopt the new photoelectric light sensor production technology, DC does some further research into its cost of financial distress. While the demand curve DC faces represents its normal demand, random monthly variation can cause demand to shift up or down unexpectedly. Given its existing bank loans, its variable costs of $ 480 per unit, no fixed manufacturing costs, and its small cash balances, DC faces a 15 percent chance of defaulting on its loans sometime over the next 24 months. If DC defaults on its loans, the owners of DC estimate the costs of default (legal costs, bank fees, lost sales, and so forth) to be $ 500,000. With the additional fixed leasing cost of the new sensor manufacturing technology, the owners of DC predict that the likelihood of defaulting on their fixed monthly commitments (bank loans and the $ 7,000 equipment lease) increases to 25 percent over the next 24 months. Prepare an analysis supporting your recommendation as to whether DC should adopt the new sensor manufacturing process or stay with their current manufacturing technology. (To simplify your analysis, assume a zero discount rate.)

  • CreatedDecember 15, 2014
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