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

Case

$1234$

Alpha Division:

Capacity in units $100,000420,000170,000320,000$

Number of units now being sold to outside customers $100,000420,000120,000320,000$

Selling price per unit to outside customers $ $70$ $ $130$ $ $175$ $ $90$

Variable costs per unit $ $58$ $ $105$ $ $140$ $ $66$

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

Beta Division:

Number of units needed annually $25,00050,00040,000124,000$

Purchase price now being paid to an outside supplier $ $67$ $ $129$ $ $175*$

$*$Before any purchase discount.

Required:

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

a$.$ What is Alpha Division's lowest acceptable transfer price?

b$.$ What is Beta Division's highest acceptable transfer price?

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

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

a$.$ What is Alpha Division's lowest acceptable transfer price?

b$.$ What is Beta Division's highest acceptable transfer price?

c$.$ 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$?$

d$.$ Assume Alpha Division offers to sell $50,000$ units to Beta Division for $$128$ per unit and that Beta Division refuses this price. What will be the loss in potential profits for the company as a whole?

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

a$.$ What is Alpha Division's lowest acceptable transfer price?

b$.$ What is Beta Division's highest acceptable transfer price?

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

d$.$ Assume Beta Division offers to purchase $40,000$ units from Alpha Division at $$160$ per unit. If Alpha Division accepts this price, would you expect its ROI to increase, decrease, or remain unchanged?

$4.$ Refer to case $4$ shown above. Assume that Beta Division wants Alpha Division to provide it with $124,000$ units of a different product from the one Alpha Division is producing now. The new product would require $$61$ per unit in variable costs and would require that Alpha Division cut back production of its present product by $46,500$ units annually. What is Alpha Division$$s lowest acceptable transfer