Chapter 13, Problem 26P

1.

To determine

Calculate the velocity and theoretical cycle time that takes to produce one model

Explanation of Solution

Cycle time: Cycle time and velocity are two operational “measures of responsiveness”. Cycle time is the span of time taken to produce a unit of output from the time the materials are received till the good is supplied to finished goods inventory. Therefore, cycle time is the time taken to produce a product.

Velocity: Velocity is the number of units of output that can be produced within a given period of time.

Calculate the theoretical velocity:

$\begin{array}{c}\text{Theoretical}\text{velocity}\text{=}\frac{\text{Theoretical}\text{output}}{\text{Cell}\text{time}}\\ \text{=}\frac{\text{27,900}\text{models}}{\text{37,200}\text{hours}}\\ \text{=}\text{0}\text{.75}\text{model}\text{per}\text{hour}\end{array}$

Calculate theoretical cycle time:

$\begin{array}{c}\text{Theoretical}\text{cycle}\text{time}\text{=}\frac{\text{Time}\text{taken}}{\text{Models}\text{produced}\text{per}\text{hour}}\\ \text{=}\frac{\text{60}\text{minutes}}{\text{0}\text{.75}\text{model}\text{per}\text{hour}}\\ \text{=}\text{80}\text{minutes}\text{per}\text{model}\end{array}$

2.

To determine

Calculate the actual velocity and the actual cycle time.

Explanation of Solution

Calculate the actual velocity:

$\begin{array}{c}\text{Actual}\text{velocity}\text{=}\frac{\text{Actual}\text{output}}{\text{Actual}\text{cell}\text{time}}\\ \text{=}\frac{\text{23,250}\text{models}}{\text{37,200}\text{hours}}\\ \text{=}\text{0}\text{.625}\text{model}\text{per}\text{hour}\end{array}$

Calculate actual cycle time:

$\begin{array}{c}\text{Actual}\text{cycle}\text{time}\text{=}\frac{\text{Time}\text{taken}}{\text{Models}\text{produced}\text{per}\text{hour}}\\ \text{=}\frac{\text{60}\text{minutes}}{\text{0}\text{.625}\text{model}\text{per}\text{hour}}\\ \text{=}\text{96}\text{minutes}\text{per}\text{model}\end{array}$

3.

To determine

Calculate the manufacturing efficiency cycle and comment on the efficiency of the operation.

Explanation of Solution

Manufacturing efficiency ratio: Manufacturing efficiency ratio is a measure of Just-In-Time (JIT) manufacturing system and it expresses the time spent in value-added activities as a percentage of total cycle time.

Calculate Manufacturing cycle efficiency:

$\begin{array}{c}\begin{array}{l}\text{Manufacturing}\\ \text{cycle}\text{efficiency}\end{array}\}\text{=}\frac{\text{Theoretical}\text{time}}{\text{Actual}\text{time}}\\ \text{=}\frac{\text{80}\text{minutes}\text{per}\text{model}}{\text{96}\text{minutes}\text{per}\text{model}}\\ \text{=}\text{0}\text{.83}\end{array}$

Therefore, from the above calculation, it is noted that, the “efficiency of the operation” is very high.

4.

To determine

Compute the budgeted conversion cost per minute, compute the conversion cost per model, compute the conversion cost per model for actual output and explain whether the product costing approach provide an incentive for the cell manager to reduce cycle time.

Explanation of Solution

Calculate budgeted conversion cost:

$\begin{array}{c}\text{Budgeted}\text{conversion}\text{cost}\text{per}\text{minute}\text{=}\frac{\text{Budgeted}\text{conversion}\text{cost}}{\left(\text{Cell}\text{time}\text{×}\text{Time}\text{taken}\right)}\\ \text{=}\frac{\text{\$6,696,000}}{\text{37,200}\text{hours}\text{×}\text{60}\text{minutes}}\\ \text{=}\frac{\text{\$6,696,000}}{\text{2,232,000}\text{minutes}}\\ \text{=}\text{\$}\text{3}\text{per}\text{minute}\end{array}$

Calculate theoretical conversion cost per model:

$\begin{array}{c}\begin{array}{l}\text{Theoretical conversion}\\ \text{cost per model}\end{array}\}\text{=}\text{Budgeted}\text{conversion}\text{cost}\text{×}\text{Theoretical}\text{cycle}\text{time}\\ \text{=}\text{\$3}\text{×}\text{80}\text{minutes}\text{per}\text{model}\\ \text{=}\text{\$240 per}\text{model}\end{array}$

Calculate actual conversion cost per model:

$\begin{array}{c}\begin{array}{l}\text{Actual}\text{conversion}\\ \text{cost}\text{per}\text{model}\end{array}\}\text{=}\text{Budgeted}\text{conversion}\text{cost}\text{×}\text{Actual}\text{cycle}\text{time}\\ \text{=}\text{\$3}\text{×}\text{96}\text{minutes}\text{per}\text{model}\\ \text{=}\text{\$288}\text{per}\text{model}\end{array}$

Yes, the cost per unit can be decreased by decreasing cycle time. The potential reduction is $48 (1) per model.

Working note:

(1)Calculate the potential reduction:

$\begin{array}{c}\text{Potential}\text{reduction}\text{=}\left(\begin{array}{l}\text{Actual}\text{conversion}\text{cost}\text{per}\text{model}-\\ \text{Theoretical}\text{conversion}\text{cost}\text{per}\text{model}\end{array}\right)\\ \text{=}\text{\$288}-\text{\$240}\\ \text{=\$48}\text{per}\text{model}\end{array}$