$23-31.$ TRANSFER PRICING, EXTERNAL MARKET, GOAL CONGRUENCE. Ballantine Corp. produces and sells lead crystal glassware. The firm consists of two divisions, commercial and specialty. The commercial division manufactures $300,000$ glasses per year. It incurs variable manufacturing costs of $$8$ per unit and annual fixed manufacturing costs of $$900,000.$ The commercial division sells $100,000$ units externally at a price of $$12$ each, mostly to department stores. It transfers the remaining $200,000$ units internally to the specialty division, which modifies the units, adds an etched design, and sells them directly to consumers online.

Ballantine Corp. has adopted a market$-$based transfer$-$pricing policy. For each glass it receives from the commercial division, the specialty division pays the weighted$-$average external price the commercial division charges its customers outside the company. The current transfer price is accordingly set at $$12.$

Eileen McCarthy, the manager of the commercial division, receives an offer from Home D$$cor$,$ a chain of upscale home furnishings stores. Home D$$cor offers to buy $20,000$ glasses at a price of $$9$ each, knowing that the entire lead crystal industry $($including Ballantine Corp.$)$ has excess capacity at this time. The variable manufacturing cost to the commercial division for the units Home D$$cor is requesting is $$8,$ and there are no additional costs associated with this offer. Accepting Home D$$cor$$s offer would not affect the current price of $$12$ charged to existing external customers.

Required

$1.$ Calculate the commercial division$$s current annual level of profit $($without the new order$).$

$2.$ Compute the change in the commercial division$$s profit if it accepts Home D$$cor$$s offer. Will Eileen McCarthy accept this offer if her aim is to maximize the commercial division$$s profit?

$3.$ Would the top management of Ballantine Corp. want the commercial division to accept the offer? Compute the change in firm$-$wide profit associated with Home D$$cor$$s offer.