Castor, a division of Gemini Corporation, is located in the United States. Its effective income tax rate is 30%. Another division of Gemini, Pollux, is located in Canada, where the income tax rate is 40%. Pollux manufactures, among other things, an intermediate product for Castor called IP- 2013. Pollux operates at capacity and makes 15,000 units of IP- 2013 for Castor each period, at a variable cost of $ 56 per unit. Assume that there are no outside customers for IP- 2013. Because the IP- 2013 must be shipped from Canada to the United States, it costs Pollux an additional $ 8 per unit to ship the IP- 2013 to Castor. There are no direct fixed costs for IP- 2013. Pollux also manufactures other products. A product similar to IP- 2013 that Castor could use as a substitute is available in the United States for $ 77 per unit.

Required
1. What is the minimum and maximum transfer price that would be acceptable to Castor and Pollux for IP- 2013, and why?
2. What transfer price would minimize income taxes for Gemini Corporation as a whole? Would Pollux and Castor want to be evaluated on operating income using this transfer price?
3. Suppose Gemini uses the transfer price from requirement 2, and each division is evaluated on its own after- tax division operating income. Now suppose Pollux has an opportunity to sell 8,000 units of IP- 2013 to an outside customer for $ 62 each. Pollux will not incur shipping costs because the customer is nearby and offers to pay for shipping. Assume that if Pollux accepts the special order, Castor will have to buy 8,000 units of the substitute product in the United States at $ 77 per unit.
a. Will accepting the special order maximize after- tax operating income for Gemini Corporation as a whole?
b. Will Castor want Pollux to accept this special order? Why or why not?
c. Will Pollux want to accept this special order? Explain.
d. Suppose Gemini Corporation wants to operate in a decentralized manner. What transfer price should Gemini set for IP- 2013 so that each division acting in its own best interest takes actions for the special order that are in the best interests of Gemini Corporation as a whole?