Question

Ag-Coop is a large farm cooperative with a number of agriculture-related manufacturing and service divisions. As a cooperative, it pays no federal income taxes. The company owns a fertilizer plant that processes and mixes petrochemical compounds into three brands of agricultural fertilizer: greenup, maintane, and winterizer. The three brands differ with respect to selling price and the proportional content of basic chemicals.

Ag-Coop’s Fertilizer Manufacturing Division transfers the completed product to the cooperative’s Retail Sales Division at a price based on the cost of each type of fertilizer plus a markup.

The Manufacturing Division is completely automated so that the only costs it incurs are the costs of the petrochemical feedstocks plus overhead that is considered fixed. The primary feedstock costs $1.80 per pound. Each 100 pounds of feedstock can produce either of the following mixtures of fertilizer.

Output Schedules (in pounds)
	A	B
Greenup	60	70
Maintane	30	10
Winterizer	10	20

Production is limited to the 820,000 kilowatt-hours monthly capacity of the dehydrator. Due to different chemical makeup, each brand of fertilizer requires different dehydrator use. Dehydrator usage in kilowatt-hours per pound of product follows:

Product	Kilowatt-Hour Usage per Pound
Greenup	42
Maintane	36
Winterizer	50

Monthly fixed costs are $84,000. The company currently is producing according to output schedule A. Joint production costs including fixed overhead are allocated to each product on the basis of weight.

The fertilizer is packed into 100-pound bags for sale in the cooperative’s retail stores. The sales price for each product charged by the cooperative’s Retail Sales Division follows:

Sales Price per Pound
Greenup	$	12.50
Maintane		11.00
Winterizer		12.40

Selling expenses are 20 percent of the sales price.

The Retail Sales Division manager has complained that the prices charged by the Manufacturing Division are excessive and that he would prefer to purchase from another supplier.

The Manufacturing Division manager argues that the processing mix was determined based on a careful analysis of the costs of each product compared to the prices charged by the Retail Sales Division.

Required:

a. Assume that joint production costs including fixed overhead are allocated to each product on the basis of weight. What is the cost per pound of each product, including fixed overhead and the feedstock cost of $1.80 per pound, given the current production schedule?

b. Assume that joint production costs including fixed overhead are allocated to each product on the basis of net realizable value if sold through the cooperative’s Retail Sales Division. What is the allocated cost per pound of each product, given the current production schedule?

Assume that joint production costs including fixed overhead are allocated to each product on the basis of weight. Calculate the operating profit under both Schedule A and Schedule B. (Do not round intermediate calculations. Round your answers to 2 decimal places.

Answer 1

a)

	Output mix	kilowatt hour per pound	kilowatt hour per 100 pounds input
Greenup	60	42	2,520
Maintane	30	36	1,080
Winterizer	10	50	500
			4,100

Maximum processing = 820,000 kwh / 4,100 kwh/100 pounds = 20,000 pounds of input

Fixed cost allocation = (84,000/20,000) = 4.20

Feedstock cost = 1.80

Joint cost = 6.00 per pound

(b) Total joint cost incurred = 84,000 + (20,000 * 1.80) = 120,000

	Quantity of each product produced
Greenup (20,000 * 60%)	12,000
Maintane (20,000 * 30%)	6,000
Winterizer(20,000 * 10%)	2,000

	Sale price per pound	Selling exp @20%	NRV/pound	Number of pounds	Total NRV
greenup	12.50	2.50	12.00	12,000	144,000
maintane	11	2.20	8.80	6,000	52,800
winterizer	12.40	2.48	9.92	2,000	19,840
				20,000	216,640

	Calculation	Allocated cost per pound
greenup	[120,000*(144,000/216,640)/12,000]	6.65per pound
maintane	[120,000*(52,800/216,640)/6,000]	4.87per pound
winterizer	[120,000*(19,840/216,640)/2,000]	5.49 per pound

(c)

Total NRV	216,640
Less: joint cost incurred	(120,000)
Profit under schedule A	96,640

Output under production schedule B

	output mix	kilowatt hr per pound	kilowatt hr per 100 pounds input
Greenup	70	42	2,940
maintane	10	36	360
winterizer	20	50	1000
			4,300

Maximum processing = 820,000 kwh / 4,300 kwh/100 pounds = 19,070pounds of input

Quantities of each product produced

Greenup (19,070 * 70%)	13,349
maintane (19,070 * 10%)	1,907
winterizer (19,070 * 20%)	3,814

Profit under production schedule B = (12.00*13,349)+(8.80*1,907)+(9.92*3,814)-(1.80*19,070) -84000 = $ 96,478.48