Northfield Manufacturing has two operating divisions in a semiautonomous organizational structure. Americas Division, based in the United States, produces a specialized memory chip that is an input to Asia Division, based in Japan. Americas Division uses idle capacity to produce the component, which has a domestic market price of $$72.$ Its variable costs are $$30$ per unit. Northfield's U$.$S$.$ tax rate is $25$ percent of income.

In addition to the transfer price for each component received from Americas, Asia Division pays an $$18$ per unit shipping fee. The chip becomes a part of its assembled product, which costs an additional $$12$ to produce and sells for an equivalent of $$138.$ Asia could purchase the component from an Asian supplier for $$60$ per unit. Northfield$$s tax rate in Japan is $30$ percent of income. Assume that Japanese tax laws permit transferring at either variable cost or market price.

Required:

a$-1.$ What are the respective profits after tax for both the Americas Division and Asia Division of Northfield Manufacturing if the transfer price is $$30?$

a$-2.$ What are the respective profits after tax for both the Americas Division and Asia Division of Northfield Manufacturing if the transfer price is $$72?$

a$-3.$ What transfer price is economically optimal for Northfield Manufacturing?