A chemical company has a batch process that takes 1,000 gallons of a raw material and transforms it into 80 pounds of X1 and 400 pounds of X2. Although the joint costs of their production are $2,400, both products are worthless at their split-off point. Additional separable costs of $700 are necessary to give X1 a sales value of $2,000 as product A. Similarly, additional separable costs of $400 are necessary to give X2 a sales value of $2,000 as product B.

You are in charge of the batch process and the marketing of both products. (Show your computations for each answer.)

1. a. Assuming that you believe in assigning joint costs on a physical basis, allocate the total profit of $500 per batch to products A and B.

b. Would you stop processing one of the products? Why?

2. a. Assuming that you believe in assigning joint costs on a net-realizable-value (relative-sales-value) basis, allocate the total operating profit of $500 per batch to products A and B. If there is no market for X1 and X2 at their split-off point, a net realizable value is usually imputed by taking the ultimate sales values at the point of sale and working backward to obtain approximated “synthetic” relative sales values at the split-off point. These synthetic values are then used as weights for allocating the joint costs to the products.

b. You have internal product-profitability reports in which joint costs are assigned on a net-realizable-value basis. Your chief engineer says that, after seeing these reports, he has developed a method of obtaining more of product B and correspondingly less of product A from each batch, without changing the per-pound cost factors. Would you approve this new method? Why? What would the overall operating profit be if 40 pounds more of B were produced and 40 pounds less of A?