Question

Mathwerks produces two electronic, handheld educational games: Fun with Fractions and Count Calculus. Data on these products follow.

Fun with Fractions Count Calculus

Production volume ………… 150,000 units 10,000 units

Components ………………… 450,000 parts 100,000 parts

Direct labor hours ………….. 15,000 DLH 2,000 DLH

Packaging materials ……….. 150,000 boxes 10,000 boxes

Shipping cartons …………… 100 units per carton 25 units per carton

Machine setups …………….. 52 setups 52 setups

Machine hours ……………… 5,000 MH 2,000 MH

Additional data from its two production departments follow.

Department Driver Cost

Assembly department

Component cost …………………….. Parts \(495,000

Assembly labor ……………………… Direct labor hours 244,800

Maintenance ………………………….. Machine hours 100,800

Wrapping department

Packaging materials ………………… Boxes \)460,800

Shipping ………………………………. Cartons 27,360

Machine setup ……………………….. Setups 187,200

Required

1. Using ABC, determine the cost of each product line.

2. What is the cost per unit ofFun with Fractions? What is the cost per unit ofCount Calculus?

3. IfCount Calculussells for $59.95 per unit, how much profit does the company earn per unit ofCount Calculussold?

4. What is the minimum price that the company should set per unit of Fun with Fractions? Explain.

Short answer

Cost per unit for Fun with Function product:$8.27

Cost per unit for Count Calculus product: $27.55

Step-by-step solution

Cost of product line

Computation of total cost of Fun with Fraction products

$\begin{array}{rcl}\mathbf{\text{Componentcost}}& \mathbf{=}& \frac{\mathbf{\text{Totalcost}}}{\mathbf{\text{TotalcomponentParts}}}\mathbf{\times }\mathbf{\text{Componentpartsusedbyproductline}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{495}\mathbf{,}\mathbf{000}}{\mathbf{450}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{100}\mathbf{,}\mathbf{000}}\mathbf{\times }\mathbf{450}\mathbf{,}\mathbf{000}\\ & \mathbf{=}& \mathbf{\$}\mathbf{405}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{rcl}\mathbf{\text{AssemblylaborCost}}& \mathbf{=}& \frac{\mathbf{\text{TotalCost}}}{\mathbf{\text{TotalDIhour}}}\mathbf{\times }\mathbf{\text{DIhourbyproductline}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{244}\mathbf{,}\mathbf{800}}{\mathbf{15}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{2000}}\mathbf{\times }\mathbf{15}\mathbf{,}\mathbf{000}\\ & \mathbf{=}& \mathbf{\$}\mathbf{216}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{rcl}\mathbf{\text{MaintenanceCost}}\mathbf{}& \mathbf{=}& \frac{\mathbf{\text{TotalCost}}}{\mathbf{\text{TotalMachineHour}}}\mathbf{\times }\mathbf{\text{Machinehourusedbyproductline}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{100}\mathbf{,}\mathbf{800}}{\mathbf{5000}\mathbf{+}\mathbf{2000}}\mathbf{\times }\mathbf{5000}\\ & \mathbf{=}& \mathbf{\$}\mathbf{72}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{rcl}\mathbf{\text{PackagingMaterialCost}}& \mathbf{=}& \frac{\mathbf{\text{TotalCost}}}{\mathbf{\text{TotalNo.ofBoxes}}}\mathbf{\times }\mathbf{\text{Totalboxesusedbyproductline}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{460}\mathbf{,}\mathbf{800}}{\mathbf{150}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{10}\mathbf{,}\mathbf{000}}\mathbf{\times }\mathbf{150}\mathbf{,}\mathbf{000}\\ & \mathbf{=}& \mathbf{\$}\mathbf{432}\mathbf{,}\mathbf{000}\end{array}$

role="math" localid="1654800908943" $\begin{array}{rcl}\mathbf{\text{Shippingcost}}& \mathbf{=}& \frac{\mathbf{\text{Totalcost}}}{\mathbf{\text{TotalCartons}}}\mathbf{\times }\mathbf{\text{Cartonsbyproductline}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{27}\mathbf{,}\mathbf{360}}{\mathbf{100}\mathbf{+}\mathbf{25}}\mathbf{\times }\mathbf{100}\\ & \mathbf{=}& \mathbf{\$}\mathbf{21}\mathbf{,}\mathbf{888}\end{array}$

$\begin{array}{rcl}\mathbf{\text{MachineSetupCost}}& \mathbf{=}& \frac{\mathbf{\text{TotalCost}}}{\mathbf{\text{TotalNo.ofsetups}}}\mathbf{\times }\mathbf{\text{Setupsusedbyproductline}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{187}\mathbf{,}\mathbf{200}}{\mathbf{52}\mathbf{+}\mathbf{52}}\mathbf{\times }\mathbf{104}\\ & \mathbf{=}& \mathbf{\$}\mathbf{93}\mathbf{,}\mathbf{6000}\end{array}$

$\begin{array}{rcl}\mathbf{\text{Totalcostforfunwithfunctionsproduct}}& \mathbf{=}& \mathbf{\text{TotalAssemblingDepartmentcostforproductline}}\mathbf{+}\mathbf{\text{TotalWrappingdepartmentcostforproductline}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{405}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{216}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{72}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{432}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{21}\mathbf{,}\mathbf{888}\mathbf{+}\mathbf{\$}\mathbf{93}\mathbf{,}\mathbf{600}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{240}\mathbf{,}\mathbf{488}\end{array}$

Computation of total cost of Count Calculus products

$\begin{array}{rcl}\mathbf{\text{ComponentCost}}& \mathbf{=}& \frac{\mathbf{\text{Totalcost}}}{\mathbf{\text{TotalComponentParts}}}\mathbf{\times }\mathbf{\text{Componentpartsusedbyproductline}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{495}\mathbf{,}\mathbf{000}}{\mathbf{450}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{100}\mathbf{,}\mathbf{000}}\mathbf{\times }\mathbf{100}\mathbf{,}\mathbf{000}\\ & \mathbf{=}& \mathbf{\$}\mathbf{90}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{rcl}\mathbf{\text{AssemblylaborCost}}& \mathbf{=}& \frac{\mathbf{\text{TotalCost}}}{\mathbf{\text{TotalMachineHour}}}\mathbf{\times }\mathbf{\text{DLhourbyproductline}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{244}\mathbf{,}\mathbf{800}}{\mathbf{15}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{2000}}\mathbf{\times }\mathbf{2}\mathbf{,}\mathbf{000}\\ & \mathbf{=}& \mathbf{\$}\mathbf{28}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{rcl}\mathbf{\text{MaintenaceCost}}& \mathbf{=}& \frac{\mathbf{\text{TotalCost}}}{\mathbf{\text{TotalMachineHour}}}\mathbf{\times }\mathbf{\text{Machinehourusedbyproductline}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{100}\mathbf{,}\mathbf{800}}{\mathbf{5000}\mathbf{+}\mathbf{2000}}\mathbf{\times }\mathbf{2000}\\ & \mathbf{=}& \mathbf{\$}\mathbf{28}\mathbf{,}\mathbf{8000}\end{array}$

$\begin{array}{rcl}\mathbf{\text{PackagingMaterialCost}}& \mathbf{=}& \frac{\mathbf{\text{TotalCost}}}{\mathbf{\text{TotalNo.ofBoxes}}}\mathbf{\times }\mathbf{\text{Totalboxesusedbyproductline}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{460}\mathbf{,}\mathbf{800}}{\mathbf{150}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{10}\mathbf{,}\mathbf{000}}\mathbf{\times }\mathbf{10}\mathbf{,}\mathbf{000}\\ & \mathbf{=}& \mathbf{\$}\mathbf{28}\mathbf{,}\mathbf{800}\end{array}$

$\begin{array}{rcl}\mathbf{\text{Shippingcost}}& \mathbf{=}& \frac{\mathbf{\text{TotalCost}}}{\mathbf{\text{TotalCartoons}}}\mathbf{\times }\mathbf{\text{Cartoonsusedbyproductline}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{27}\mathbf{,}\mathbf{360}}{\mathbf{100}\mathbf{+}\mathbf{25}}\mathbf{\times }\mathbf{25}\\ & \mathbf{=}& \mathbf{\$}\mathbf{5}\mathbf{,}\mathbf{472}\end{array}$

$\begin{array}{rcl}\mathbf{\text{Machinesetupcost}}& \mathbf{=}& \frac{\mathbf{\text{Totalcost}}}{\mathbf{\text{Totalno.ofsetups}}}\mathbf{\times }\mathbf{\text{Setupsusedbyproductline}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{187}\mathbf{,}\mathbf{200}}{\mathbf{52}\mathbf{+}\mathbf{52}}\mathbf{\times }\mathbf{104}\\ & \mathbf{=}& \mathbf{\$}\mathbf{93}\mathbf{,}\mathbf{600}\end{array}$

$\begin{array}{rcl}\mathbf{\text{TotalcostforFunwithfunctionsproduct}}& \mathbf{=}& \mathbf{\text{TotalAssemblingDepartmentcostforproductline}}\mathbf{+}\mathbf{\text{TotalWrappingdepartmentcostforproductline}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{90}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{28}\mathbf{,}\mathbf{800}\mathbf{+}\mathbf{\$}\mathbf{28}\mathbf{,}\mathbf{800}\mathbf{+}\mathbf{\$}\mathbf{5}\mathbf{,}\mathbf{472}\mathbf{+}\mathbf{\$}\mathbf{93}\mathbf{,}\mathbf{600}\\ & \mathbf{=}& \mathbf{\$}\mathbf{275}\mathbf{,}\mathbf{472}\end{array}$

Cost per unit

$\begin{array}{rcl}\mathbf{\text{CostperunitforFunwithFunctionsproduct}}& \mathbf{=}& \frac{\mathbf{\text{TotalCostforproductline}}}{\mathbf{\text{Totalno.ofproducts}}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{240}\mathbf{,}\mathbf{488}}{\mathbf{150}\mathbf{,}\mathbf{000}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{8}\mathbf{.}\mathbf{27}\end{array}$

$\begin{array}{rcl}\mathbf{\text{CostperunitforCountCalculusproduct}}& \mathbf{=}& \frac{\mathbf{\text{TotalCostforproductline}}}{\mathbf{\text{Totalno.ofproducts}}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{275}\mathbf{,}\mathbf{472}}{\mathbf{10}\mathbf{,}\mathbf{000}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{27}\mathbf{.}\mathbf{55}\end{array}$

Profit per unit

$\begin{array}{rcl}\mathbf{\text{Profitperunitforcountcalculusproduct}}& \mathbf{=}& \mathbf{\text{Sellingpriceperbottle}}\mathbf{-}\mathbf{\text{Costperbottle}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{59}\mathbf{.}\mathbf{95}\mathbf{-}\mathbf{\$}\mathbf{27}\mathbf{.}\mathbf{55}\\ & & \mathbf{\$}\mathbf{32}\mathbf{.}\mathbf{4}\end{array}$

Minimum price per unit

Minimum price for the Fun with Function product is the rate at which company incurs neither any profit nor any loss. Thus the minimum price must be equal to the cost of the product.

In the given case, the minimum price for Fun with Function product product must be $8.27 per bottle