Question

  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
	1	2	3	4
Alpha Division:
Capacity in units	82,000	402,000	152,000	302,000
Number of units now being sold to outside customers	82,000	402,000	102,000	302,000
Selling price per unit to outside customers	$ 34	$ 94	$ 85	$ 54
Variable costs per unit	$ 22	$ 69	$ 50	$ 30
Fixed costs per unit (based on capacity)	$ 6	$ 15	$ 20	$ 9
Beta Division:
Number of units needed annually	7,000	32,000	22,000	120,400
Purchase price now being paid to an outside supplier	$ 31	$ 93	$ 85*	—

*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 32,000 units to Beta Division for $92 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 22,000 units from Alpha Division at $70 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 120,400 units of a different product from the one Alpha Division is producing now. The new product would require $25 per unit in variable costs and would require that Alpha Division cut back production of its present product by 45,150 units annually. What is Alpha Division’s lowest acceptable transfer price?

Answer 1

 

Working notes is given here

Case 1

Case 1

Identify the lowest and highest acceptable transfer price

Division Alpha

Lowest acceptable transfer price

$32

Selling price per unit

$34

Highest acceptable transfer price

$31

Less: Variable cost per unit

$22

Contribution margin per unit

$12

Identify the range of acceptable transfer price (if any)

Division Alpha

Division Beta

Variable Cost Less :Commission $2

$20

Market price per unit

$31

There is not a range of acceptable of transfer prices

Add :Contribution margin forgone

$12

There is a range of acceptable transfer prices as shown below

Transfer price

$32

Minimum transfer price per unit

$32

Maximum Transfer price

$31

$0

<=

Transfer price

<=

$0

There is not a range of acceptable of transfer prices

Will the mangers agree to the trade

No

Case 2

Case 2

Identify the lowest and highest acceptable transfer price

Lowest acceptable transfer price

$89

Division Alpha

Highest acceptable transfer price

$93

Selling price per unit

$94

Less: Variable cost per unit

$69

Contribution margin per unit

$25

Identify the range of acceptable transfer price (if any)

Division Alpha

Division Beta

Variable Cost Less :Shipping cost $5

$64

Market price per unit

$93

There is a range of acceptable transfer prices as shown below

Add: Contribution forgone

$25

Transfer price

$89

$89

<=

Transfer price

<=

$93

Minimum transfer price per unit

$89

Maximum Transfer price

$93

Will the mangers agree to the trade

Yes

Outside purchase price

$93

Division Beta has to purchase at this price

Less: Division Alpha transfer price

$89

minimum transfer price

Loss per unit- external purchase

$4

a

Loss in potential profits for the company

$128,000

Total units

32,000

b

units as given

Loss in Potential profits for

company as a whole

$128,000

a*b

Working notes is given above for each of the requirement with the calculations

• Explanation for step 1

When there is no surplus capacity the contribution margin forgone is the opportunity cost involved and it is relevant cost

Step 2/2

 

Case 3

Case 3

Since capacity is not fully utilized there is no opportunity loss by selling to

Identify the lowest and highest acceptable transfer price

Division Beta

Lowest acceptable transfer price

$50.00

Highest acceptable transfer price

$78.20

Division Alpha

Division Beta

Variable Cost per unit

$50.00

Market price

$85.00

Identify the range of acceptable transfer price (if any)

Less: Discount @ 8%

$6.80

Net purchase price

$78.20

There is a range of acceptable transfer prices as shown below

Minimum transfer price per unit

$50.00

Maximum Transfer price

$78.20

$50.00

<=

Transfer price

<=

$78.20

Since capacity is unused and any purchase by Beta division above variable cost

Will the mangers agree to the trade

will increase contribution

Yes

Purchase price per unit

$70

as given

Less: minimum transfer price

$50

Contribution margin per unit

$20

a

Division A's ROI should

Units transferred

22,000

b

Increase

Total contribution margin increase

$440,000

a*b

Case 4

Case 4

Lowest acceptable transfer price

$34.00

Production cut units

45,150

a

Contribution margin /unit ($54-$30)

$24

b

Total contribution margin forgone

$1,083,600

a*b

Lowest transfer price

Variable Cost per unit

$25.00

as given

Add: Contribution margin forgone

$9.00

($1,083,600/120,400)

Lowest acceptable transfer price

$34.00

per unit

Working notes is given above for each of the requirement with the calculations

• Explanation for step 2

Fixed costs are not relevant costs in setting the transfer price

Final answer

Answer is given in step 1 and step 2 as per required format with working notes and explanation

$34