Cost Allocation—Joint Products and By-Product. Brooks Corporation produces three products, Alpha, Beta, and Gamma. Alpha and Gamma are joint products; Beta is a by-product of Alpha. No joint cost is to be allo¬ cated to the by-product. The production processes for a given year are as follows: LO5

(a) In Department 1, 110,000 pounds of material Rho are processed, at a total cost of $120,000. After process¬ ing, 60% of the units are transferred to Department 2, and 40% of the units (now Gamma) are transferred to Department 3-

(b) In Department 2, the material is further processed at a total additional cost of $38,000. Seventy percent of the units (now Alpha) are transferred to Department 4 and 30% emerge as Beta, the by-product, to be sold at $1.20 per pound. The marketing expense related to Beta is $8,100.

(c) In Department 4, Alpha is processed at a total additional cost of $23,660. After processing, Alpha is ready for sale at $5 per pound.

(d) In Department 3, Gamma is processed at a total additional cost of $165,000. In this department, a normal loss of units of Gamma occurs, which equals 10% of the good output of Gamma. The remaining good out¬ put is sold for $12 per pound.

Required:

(1) Prepare a schedule showing the allocation of the $120,000 joint cost between Alpha and Gamma, using the market value at split-off point and treating the net realizable value of Beta as an addition to the sales value of Alpha.

(2) Prepare a statement of gross profit for Alpha, independent of the answer to requirement 1, assuming that:

(a) $102,000 of total joint cost is appropriately allocated to Alpha.

(b) 48,000 pounds of Alpha and 20,000 pounds of Beta are available for sale.

(c) During the year, sales of Alpha were 80% of the pounds available for sale. There was no beginning inventory.

(d) The net realizable value of Beta available for sale is to be deducted from the cost of producing Alpha. The ending inventory of Alpha is to be based on the net cost of production.

(e) All other costs, sales prices, and marketing expenses are those presented in the facts of the original problem.