Alpha and Beta are divisions within the same company. The managers of both divisions are evaluated based on their return on investment $($ROI$).$ Assume the following information for the two divisions:

Case

$1234$

Alpha Division:

Capacity in units $94,000414,000164,000314,000$

Number of units now being sold to outside customers $94,000414,000114,000314,000$

Selling price per unit to outside customers $ $58$ $ $118$ $ $145$ $ $78$

Variable costs per unit $ $46$ $ $93$ $ $110$ $ $54$

Fixed costs per unit $($based on capacity$)$ $ $6$ $ $15$ $ $20$ $ $9$

Beta Division:

Number of units needed annually $19,00044,00034,000122,800$

Purchase price now being paid to an outside supplier $ $55$ $ $117$ $ $145*$

$*$Before any purchase discount.

Required:

Refer to case $1$ shown above. Alpha Division can avoid $$2$ per unit in commissions on any sales to Beta Division.

What is Alpha Division's lowest acceptable transfer price?

What is Beta Division's highest acceptable transfer price?

What is the range of acceptable transfer prices $($if any$)$ between the two divisions? Will the managers agree to a transfer?

Refer to case $2$ shown above. A study indicates Alpha Division can avoid $$5$ per unit in shipping costs on any sales to Beta Division.

What is Alpha Division's lowest acceptable transfer price?

What is Beta Division's highest acceptable transfer price?

What is the range of acceptable transfer prices $($if any$)$ between the two divisions? Would you expect any disagreement between the two divisional managers over what the exact transfer price should be$?$

Assume Alpha Division offers to sell $44,000$ units to Beta Division for $$116$ per unit and Beta Division refuses this price. What will be the company$$s loss in potential profits?

Refer to case $3$ shown above. Assume Beta Division is now receiving an $8\%$ price discount from the outside supplier.

What is Alpha Division's lowest acceptable transfer price?

What is Beta Division's highest acceptable transfer price?

What is the range of acceptable transfer prices $($if any$)$ between the two divisions? Will the managers agree to a transfer?

Assume Beta Division offers to purchase $34,000$ units from Alpha Division at $$130$ per unit. If Alpha Division accepts this price, would you expect its ROI to increase, decrease, or remain unchanged?

Refer to case $4$ shown above. Assume Beta Division wants Alpha Division to provide it with $122,800$ units of a different product from the one Alpha Division is producing now. The new product would require $$49$ per unit in variable costs and would require Alpha Division to cut back production of its present product by $46,050$ units annually. What is Alpha Division$$s lowest acceptable transfer price?