Mark Ahren is an award-winning potter whose primary products are custom-designed cups and mugs in unique shapes. Mark estimates that the variable costs (clay bisque, pigments, glaze, and so on) are $3.50 per mug. He estimates 75% of this cost relates to materials, and the other 25% to labor and variable overhead. The average mug weighs a pound and sells for $13.

Mark also incurs costs for operating his office ($50,750 per year), travel to fairs, and so on ($26,250), and, most important, for firing his custom-built, high-temperature oven ($77,000).

For the past couple of years, Mark has expanded his product line to include larger items such as water pitchers and vases. Pitchers weigh in at 2 pounds per unit, have a variable cost of $6 per unit, and retail for $20. Corresponding data for vases are 3 pounds, $8 per unit, and $24 per unit. Mark believes that materials constitute 75% of the variable cost for these items as well. For the coming year, he estimates producing 29,000 mugs and 3,000 units each of the larger items, or 35,000 pieces in total.

Mark emphasizes the importance of having a high-quality reliable oven in his line of work. Indeed, he tells you that the oven capacity essentially controls what he could do in terms of product volume. In particular, he claims that he could easily hire more labor to mix the clay and do other miscellaneous tasks. While it might take several months, he also believes that he could also expand his sales and administrative capacity by hiring appropriate staff. However, replacing the oven will take close to two years. In addition to the substantial investment, Mark has to coordinate with the manufacturer so that the oven meets Mark’s exacting specifications. Mark notes that he started with a smallest possible oven, with a capacity of 25,000 pounds. Each replacement oven has been larger, although he thinks he might have reached the limit for a single oven.

Finally, because of the time required to set up, load, and unload the oven, Mark could fire the oven only 200 times (or about 40,000 pounds) per year. He could produce 250 mugs, 50 vases, or 100 pitchers per firing. Mark is careful to note that the actual number of firings in any given year might be a bit higher or lower. Moreover, he observes that the time required for a firing depends on the weight of the products fired. Because most firings have a combination of mugs, vases, and pitchers, the actual time per firing of the oven varies quite a bit.

Required:

a. Suppose Mark allocates all overhead to products using the number of units as the allocation basis. Determine the unit contribution and unit profit margin for each of Mark’s three product lines. What is the implication for which products to emphasize and which to deemphasize?

b. Repeat requirement (a) assuming that Mark allocates all overhead using the number of pounds as the allocation basis. What is the implication for which products to emphasize and which to deemphasize?

c. Continue with pounds as the allocation basis. For each product, what value could Mark attach to a unit in inventory? Recall that Mark would employ this unit for computing reported income, meaning that the allocation choices must conform with GAAP.

d. Is there a clear choice for the basis (pounds versus units) that Mark should choose for valuing inventory? for assessing product profitability? Justify your answer.

e. Mark also learns about activity-based costing. Again, he understands the logic of this method. He therefore wants to compute product profitability using the expected number of firings (200) to allocate oven-related costs and the number of units to allocate selling costs. He wants to allocate all other costs at the rate of $0.10 per revenue dollar. Perform this computation and rank order products as per their ABC profit margin.

f. Compute Mark’s total income using ABC to allocate costs. Why do you expect this income to be the same (subject to rounding) as the income computed when you use the number of units to allocate costs?

g. Under what conditions would you expect the ABC income you computed for part (g) to differ from the income reported under GAAP?

h. By now, Mark is thoroughly confused as to which of his three products is the most profitable, and deserves more emphasis in his product mix. Please be sure to outline the implicit assumptions and requirements for each of the methods (the two volume-based allocations, inventory value, and ABC).