Chapter 1, Problem 13P

a)

Summary Introduction

To determine: Productivity change for Person CL’s bakery in loaves per dollar and with an increase in labor cost.

Introduction: Productivity is a measure of the effectiveness of an individual, systems, machinery and other equipment that are used in converting inputs into outputs. In all organizations, productivity is an important determinant to know cost efficiency.

Answer to Problem 13P

The productivity change with the existing labor force will be 0.293 loaves per dollar and 0.293 loaves per dollar with the new labor force.

Explanation of Solution

Given information: Person CL’s bakery makes 1,500 loaves of bread in a month. Their employees are paid $8 per hour and their total labor hours is 640 hours.

Formula to calculate productivity change:

$\text{Productivity change}=\frac{\text{Total loaves produced in a month}}{\left(\text{Total labor hour}\times \text{Total wages per hour}\right)}$

Determine the productivity change with the existing process:

The productivity change is calculated by dividing the total loaves produced in a month by the result of the total labor hour multiplied to wages per hour.

$\begin{array}{c}\text{Productivity change}=\frac{\text{Total loaves produced in a month}}{\left(\text{Total labor hour}\times \text{Total wages per hour}\right)}\\ =\frac{\text{1,500 loaves}}{\left(\text{640 hours}\times \text{\$8}\right)}\\ =\frac{\text{1,500 loaves}}{5,120}\\ =0.293\text{loaves per dollar}\end{array}$ (1)

The productivity change with the existing labor force is 0.293 loaves per dollar.

Determine the productivity change with the new process:

Given information:

Person CL’s bakery increases its productivity to 1,875 loaves of bread in a month. Employees are paid $8 per hour and total labor hours are 800 hours.

$\begin{array}{c}\text{Productivity change}=\frac{\text{Total loaves produced in a month}}{\left(\text{Total labor hour}\times \text{Total wages per hour}\right)}\\ =\frac{\text{1,875 loaves}}{\left(\text{800 hours}\times \text{\$8}\right)}\\ =\frac{\text{1,875 loaves}}{6,400}\\ =0.293\text{loaves per dollar}\end{array}$ (2)

The productivity change with the new labor force is 0.293 loaves per dollar.

b)

Summary Introduction

To determine: The newproductivity change for Person CL’s bakery in loaves per dollar and with an increase in investment.

Answer to Problem 13P

The new productivity for Person CL’s bakery with the existing process is 0.293 loaves per dollar and with the new process being 0.359 loaves per dollar.

Explanation of Solution

Given information:

Person CL’s bakery makes 1,500 loaves of bread in a month. The employees are paid $8 per hour and total labor hours are 640 hours.

Formula to calculate productivity change:

$\text{Productivity change}=\frac{\text{Total loaves produced in a month}}{\left(\text{Total labor hour}\times \text{Total wages per hour}\right)}$

Determine the productivity change with existing process:

The productivity change is calculated by dividing the total loaves produced in a month by the result of the total labor hour multiplied with the wages per hour.

$\begin{array}{c}\text{Productivity change}=\frac{\text{Total loaves produced in a month}}{\left(\text{Total labor hour}\times \text{Total wages per hour}\right)}\\ =\frac{\text{1,500 loaves}}{\left(\text{640 hours}\times \text{\$8}\right)}\\ =\frac{\text{1,500 loaves}}{5,120}\\ =0.293\text{loaves per dollar}\end{array}$ (3)

The productivity change with the existing labor force is 0.293 loaves per dollar.

Determine the productivity change with new process:

Given information: Person CL’s bakery increases its productivity to 1,875 loaves of bread in a month. The employees are paid $8 per hour, the total labor hours is 640 hours and an investment of $100 per month is made.

$\begin{array}{c}\text{Productivity change}=\frac{\text{Total loaves produced in a month}}{\left(\text{Total labor hour}\times \text{Total wages per hour}\right)}\\ =\frac{\text{1,875 loaves}}{\left(\text{640 hours}\times \text{\$8}\right)+\$100}\\ =\frac{\text{1,875 loaves}}{5,220}\\ =0.359\text{loaves per dollar}\end{array}$ (4)

The productivity change with new process is 0.359 loaves per dollar.

c)

Summary Introduction

To determine: The percentage of productivity change for labor and investment.

Answer to Problem 13P

The percentage of productivity change for labor is 0% and for investment is 22.5%.

Explanation of Solution

Labor:

Formula to calculate percentage of productivity change:

$\text{Percentage change}=\frac{\text{Change in productivity value}-\text{Intital productivity value}}{\text{Intital productivity value}}\times 100$

Calculate percentage change for labor:

The percentage change of productivity is calculated by subtracting the initial productivity value from change in productivity value and dividing the result by the initial productivity value.

The change in productivity value is 0.293 (refer to equation (2)) and the initial productivity value is 0.293 (refer to equation (1)).

$\begin{array}{c}\text{Percentage change}=\frac{\text{Change in productivity value}-\text{Intital productivity value}}{\text{Intital productivity value}}\times 100\\ =\frac{\text{0}\text{.293}-\text{0}\text{.293}}{\text{0}\text{.293}}\times 100\\ =\frac{0}{0.293}\times 100\\ =0\%\end{array}$

Hence, the percentage of productivity change for labor is 0%.

Investment:

Formula to calculate percentage of productivity change:

$\text{Percentage change}=\frac{\text{Change in productivity value}-\text{Intital productivity value}}{\text{Intital productivity value}}\times 100$

Calculate percentage change for investment:

The percentage change of productivity is calculated by subtracting the initial productivity value from the change in productivity value and dividing the result by the initial productivity value.

The change in the productivity value is 0.359 (refer to equation (4)) and the initial productivity value is 0.293 (refer to equation (3)).

$\begin{array}{c}\text{Percentage change}=\frac{\text{Change in productivity value}-\text{Intital productivity value}}{\text{Intital productivity value}}\times 100\\ =\frac{\text{0}\text{.359}-\text{0}\text{.293}}{\text{0}\text{.293}}\times 100\\ =\frac{0.066}{0.293}\times 100\\ =22.5\%\end{array}$

Hence, the percentage of productivity change for investment is 22.5%.