Chapter 7.S, Problem 9P

a)

Summary Introduction

To determine: The unit cost for 20 units.

Introduction: Learning curve is referred as the cost curve, experience curve, efficiency curve or productivity curve. The leaving curve gives information about the cost, efficiency, productivity and performance of an organization.

Answer to Problem 9P

The unit cost for 20 units is $80.31.

Explanation of Solution

Given information:

$\begin{array}{c}\text{Laborcost}=\text{\$8}\text{.50}\text{per}\text{hour}\\ \text{Setup}\text{cost}=\text{\$50}\text{.00}\\ \text{Material}\text{cost}=\text{\$20}\text{.00}\text{per}\text{unit}\\ \text{Learning}\text{curve}=\text{90\%}\end{array}$

$\begin{array}{c}\text{Overhead}=\text{50\%}\text{of}\text{labor,}\text{materials}\text{and}\text{setup}\text{cost}\\ {\text{T}}_{\text{1}}=\text{5}\text{hours}\\ \text{Purchase}\text{cost}=\text{\$88}\text{.50}\text{per}\text{unit}\end{array}$

Formula:

${\displaystyle \sum {\text{T}}_{\text{n}}}={\text{T}}_{\text{1}}\times \text{Unit}\text{factor}$

Calculation of unit cost for 20 units:

The time to compute the unit cost for 20 units is to compute the average cost for 20 units. It can be computed by finding labor cost, material cost, overhead cost and total cost. From the total cost, the average cost is computed.

Estimation of labor, material, overheads and total cost:

At 90% learning curve, the unit factor for 20 unit is 14.608 (using learning curve coefficient table)

$\begin{array}{c}{\text{T}}_{1-20}={\text{T}}_{\text{1}}\text{×14}\text{.608}\\ =\text{5}\times \text{14}\text{.608}\\ =\text{73}\text{.04}\text{hours}\end{array}$

The time for completing the 20 units is calculated by multiplying 5 with the unit factors 14.608 which yields 73.04 hours.

$\begin{array}{c}\text{Labor}\text{cost}=\text{73}\text{.04}\text{hours}\times \text{8}\text{.50}\text{per}\text{hour}\\ =\text{\$620}\text{.84}\end{array}$

The labor cost is calculated by multiplying 73.045 hours with 8.50 which yields $620.84.

$\begin{array}{c}\text{Material}\text{cost}=20\text{units}\times \text{\$20}\text{per}\text{unit}\\ =\text{\$400}\text{.00}\end{array}$

Material cost is calculated by multiplying 20 units with $20 per unit which yields $400.

$\begin{array}{c}\text{Overhead}\text{cost}=0.50\times \left(\$620.84+\$400.00+\$50.0\right)\\ =\text{\$535}\text{.42}\end{array}$

The overhead cost calculated by taking 50% of labor, material and setup cost which accounts to $535.42

$\begin{array}{c}\text{Total}\text{cost}=\text{Setup}\text{cost}+\text{Labor}\text{cost}+\text{Material}\text{cost}+\text{Overheadcost}\\ =\text{\$50}+\text{\$620}\text{.84}+\text{\$535}\text{.42+\$400}\text{.00}\\ =\text{\$1,606}\text{.26}\end{array}$

The total cost is calculated by summing up labor cost, material cost and overhead cost which is adding $50, $620.84, $535.42 and $400.00 which yields $1,606.26.

$\begin{array}{c}\text{Average}\text{cost}\text{per}\text{unit}=\frac{\text{\$1,606}\text{.26}}{\text{20}}\\ =\text{\$80}\text{.31}\end{array}$

The average cost per unit is calculated by dividing $1,606.26 with 20 which yields $80.31.

Hence, the unit cost for 20 units is $80.31.

b)

Summary Introduction

To determine: The minimum production quantity necessary to make the production cost less than the purchase cost.

Introduction: Learning curve is referred as the cost curve, experience curve, efficiency curve or productivity curve. The leaving curve gives information about the cost, efficiency, productivity and performance of an organization.

Answer to Problem 9P

The minimum production quantity necessary to make the production cost less than the purchase cost is $88.46.

Explanation of Solution

Given information:

$\begin{array}{c}\text{Laborcost}=\text{\$8}\text{.50}\text{per}\text{hour}\\ \text{Setup}\text{cost}=\text{\$50}\text{.00}\\ \text{Material}\text{cost}=\text{\$20}\text{.00}\text{per}\text{unit}\\ \text{Learning}\text{curve}=\text{90\%}\end{array}$

$\begin{array}{c}\text{Overhead}=\text{50\%}\text{of}\text{labor,}\text{materials}\text{and}\text{setup}\text{cost}\\ {\text{T}}_{\text{1}}=\text{5}\text{hours}\\ \text{Purchase}\text{cost}=\text{\$88}\text{.50}\text{per}\text{unit}\end{array}$

Formula:

${\displaystyle \sum {\text{T}}_{\text{n}}}={\text{T}}_{\text{1}}\times \text{Unit}\text{factor}$

Calculation of minimum production quantity necessary to make the production cost less than the purchase cost:

The production cost per unit is $80.31 per unit for 20 units and it is less than the purchase cost which is $88.50 per unit. By trial and error approach the numbers which accounts to less than the purchase cost is computed which are 10 units.

Estimation of labor, material, overheads and total cost:

At 90% learning curve, the unit factor for 10 unit is 7.994 (using learning curve coefficient table)

$\begin{array}{c}{\text{T}}_{1-10}={\text{T}}_{\text{1}}\text{×7}\text{.994}\\ =\text{5}\times \text{7}\text{.994}\\ =\text{39}\text{.97}\text{hours}\end{array}$

The time for completing 10 units is calculated by multiplying 5 with the unit factors 7.994 which yields 39.97 hours.

$\begin{array}{c}\text{Labor}\text{cost}=39.97\text{hours}\times \text{8}\text{.50}\text{per}\text{hour}\\ =\text{\$339}\text{.75}\end{array}$

The labor cost is calculated by multiplying 39.97 hours with 8.50 which yields $339.75.

$\begin{array}{c}\text{Material}\text{cost}=10\text{units}\times \text{\$20}\text{per}\text{unit}\\ =\text{\$200}\text{.00}\end{array}$

Material cost is calculated by multiplying 10 units with $20 per unit which yields $200.

$\begin{array}{c}\text{Overhead}\text{cost}=0.50\times \left(\$339.75+\$200.00+\$50.0\right)\\ =\text{\$294}\text{.88}\end{array}$

The overhead cost calculated by taking 50% of labor, material and setup cost which accounts to $294.88

$\begin{array}{c}\text{Total}\text{cost}=\text{Setup}\text{cost}+\text{Labor}\text{cost}+\text{Material}\text{cost}+\text{Overheadcost}\\ =\text{\$50}+\$339.75+\text{\$294}\text{.88}+\text{\$200}\text{.00}\\ =\text{\$884}\text{.63}\end{array}$

The total cost is calculated by summing up labor cost, material cost and overhead cost which is adding $50, $339.75, $294.88 and $200 which yields $884.63.

$\begin{array}{c}\text{Average}\text{cost}\text{per}\text{unit}=\frac{\text{\$884}\text{.63}}{\text{10}}\\ =\text{\$88}\text{.46}\end{array}$

The average cost per unit is calculated by dividing $884.63 with 10 which yields $88.46 which is less than $88.50.

Hence, the minimum production quantity necessary to make the production cost less than the purchase cost is $88.46.