Question

Alton Inc. is working at full production capacity producing 26,000 units of a unique product. Manufacturing costs per unit for the product are as follows: Direct materials $ 10 Direct labor 9 Manufacturing overhead 11 Total manufacturing cost per unit $ 30 The per-unit manufacturing overhead cost is based on a $5 variable cost per unit and $156,000 fixed costs. The nonmanufacturing costs, all variable, are $8 per unit, and the sales price is $45 per unit. Sports Headquarters Company (SHC) has asked Alton to produce 6,500 units of a modification of the new product. This modification would require the same manufacturing processes. However, because of the nature of the proposed sale, the estimated nonmanufacturing costs per unit are only $4 (not $8). Alton would sell the modified product to SHC for $35 per unit.

Required: Suppose that Alton Inc. had been working at less than full capacity to produce 21,400 units of the product when SHC made the offer. What is the minimum price per unit that Alton should accept for the modified product under these conditions?

Answer 1

Direct materials = $ 10 per unit Direct labor = $9 per unit Variable Manufacturing overhead = $5 per unit Variable Non-manufacturing costs= $8 per unit

Total variable cost per unit = 10 + 9 + 5 + 8

= $32     Sales price = $45 per unit

Contribution margin per unit = Selling price per unit - Variable cost per unit

= 45 - 32

= $13

Current production = 21,400 units

Maximum production capacity = 26,000 units

Special order = 6,500 units

Hence, to fulfill special order, Alton will have have to sacrifice its current production by = 21,400 + 6,500 - 26,000

= 1,900 units

Hence, loss of contribution margin = Current production sacrificed x Contribution margin per unit

= 1,900 x 13

= $24,700

Total variable cost per unit of modified product = 10 + 9 + 5 + 4

= $28

Minimum price of the modified product should cover the variable costs and loss of contribution margin

Hence, total sales value of modified product = Total variable costs + loss of contribution margin

= 6,500 x 28 + 24,700

= $206,700

Minimum price per unit that Alton should accept for the modified product = Total sales value of modified product/Number of units of modified product

= 206,700/6,500

= $31.8