Sierra Inc. consists of a semiconductor division and a process-control division, each of which operates as an independent profit center. The semiconductor division employs craftsmen who produce two different electronic components: the new high performance Xcel-chip and an older product called the Dcel-chip. These products have the following cost characteristics:
..........................................Xcel-chip ..............Dcel-chip
Direct materials ..............................$ 10 .....................$ 8
Direct manufacturing labor:
4 hours × $25; 2 hours × $25 ................100 ......................50
Due to the high skill level necessary for the craftsmen, the semiconductor division's capacity is set at 55,000 hours per year.
Maximum demand for the Xcel-chip is 13,750 units annually, at a price of $130 per chip. There is unlimited demand for the Dcel-chip at $65 per chip.
The process-control division produces only one product, a process-control unit, with the following cost structure:
■ Direct materials (circuit board): $80
■ Direct manufacturing labor (3.5 hours * $10): $35
The current market price for the control unit is $125 per unit.
A joint research project has just revealed that a single Xcel-chip could be substituted for the circuit board currently used to make the process-control unit. The direct manufacturing labor cost of the process control unit would be unchanged. The improved process-control unit could be sold for $185.
Required
1. Calculate the contribution margin per direct-labor hour of selling Xcel-chip and Dcel-chip. If no transfers of Xcel-chip are made to the process-control division, how many Xcel-chips and Dcel-chips should the semiconductor division manufacture and sell? What would be the division's annual contribution margin? Show your computations.
2. The process-control division expects to sell 1,250 process-control units this year. From the viewpoint of Sierra Inc. as a whole, should 1,250 Xcel-chips be transferred to the process-control division to replace circuit boards? Show your computations.
3. What transfer price, or range of prices, would ensure goal congruence among the division managers? Show your calculations.
4. If labor capacity in the semiconductor division were 60,000 hours instead of 55,000, would your answer to requirement 3 differ? Show your calculations.