Chapter 10, Problem 9PA

(a)

Summary Introduction

Interpretation: The annual capacity with a single eight hour shift is to be calculated.

Concept Introduction:

The annual capacityis the maximum level of output that a company is able to make a product or provide a service in a year.

Output per day is calculated by,

  $\text{Output}\text{per}\text{day}=\frac{\text{Total}\text{time}\text{available}}{\text{Time}\text{to}\text{make}\text{one}\text{unit}}$

The capacity is given by,

  $\text{Capacity = Number}\text{of}\text{machines ×Working}\text{days ×Output}\text{per}\text{}\text{day}$

Explanation of Solution

Given information:

Fixed cost for one shift is $60,000.

Unit variable cost is $7.

Selling price is $12.

Number of machines is 6.

Number of working days in year is 340.

Processing time per unit is 40 minutes.

The annual capacity with a single eight hour shift calculation is shown below:

  $\begin{array}{c}\text{Output}\text{per}\text{day}=\frac{\text{Total}\text{time}\text{available}}{\text{Time}\text{to}\text{make}\text{one}\text{unit}}\\ =\frac{8\text{hour}\times 60\text{minutes}}{40\text{minutes}}\\ =12\text{units}\end{array}$

The capacity is calculated as follows:

  $\begin{array}{c}\text{Capacity}=\text{Number}\text{of}\text{machines}\times \text{Working}\text{days}\times \text{Output}\text{per}\text{}\text{day}\\ =6\times 340\times 12\\ =24480\text{units}\end{array}$

Thus, the capacity of plant is 24480 units per year.

(b)

Summary Introduction

Interpretation: The capacity with two shifts is to be calculated.

Concept Introduction:

The annual capacityis the maximum level of output that a company is able to make a product or provide a service in a year.

The formula to calculate the output per day is given by,

  $\text{Output}\text{per}\text{day}=\frac{\text{Total}\text{time}\text{available}}{\text{Time}\text{to}\text{make}\text{one}\text{unit}}$

Explanation of Solution

The annual capacity with a single eight hour shift is calculated as shown below:

  $\begin{array}{c}\text{Output}\text{per}\text{day}=\frac{\text{Total}\text{time}\text{available}}{\text{Time}\text{to}\text{make}\text{one}\text{unit}}\\ =\frac{8\text{hour}\times 2\times 60\text{minutes}}{40\text{minutes}}\\ =24\text{units}\end{array}$

Determine the capacity as follows.

  $\begin{array}{c}\text{Capacity}=\text{Number}\text{of}\text{machines}\times \text{Working}\text{days}\times \text{Output}\text{per}\text{}\text{day}\\ =6\times 340\times 24\\ =48960\text{units}\end{array}$

Thus, the capacity of plant is 48960 unit per year.

(c)

Summary Introduction

Interpretation: The break-even volume with a single shift operation is to be calculated.

Concept Introduction:

Break-even point is the no profit no loss situation.

Breakevenvolumeis the amount of product that needs to be produced and sold to cover total costs of production.

Explanation of Solution

Calculate the break-even volume with one shiftas shown below.

  $\begin{array}{c}\text{Break}\text{even}\text{point}=\frac{\text{Fixed}\text{cost}}{\text{Selling}\text{price}-\text{Variable}\text{cost}}\\ =\frac{\$60000}{\$12-\$7}\\ =12,000\text{units}\end{array}$

Thus, the break-even volume with one shift is $12000 units.

(d)

Summary Introduction

Interpretation: The maximum revenue with a single shift is to be calculated.

Concept Introduction:

Revenueis defined as the income of a company that is generated from its normal business activities, such as the sale of goods and services to customers.

Explanation of Solution

The maximum revenue per shift is calculated by using the following formula:

  $\begin{array}{c}\text{Revenue}=\text{Capacity}\text{with}\text{single}\text{shift}\times \text{Sales}\text{per}\text{unit}\\ =\$24,800\times \$12\\ =\$297,600\end{array}$

Thus, the revenue is $297,600 units.

(e)

Summary Introduction

Interpretation: The break-even volume with a two shift operation is to be calculated.

Concept Introduction:

Break-even point is the no profit, no loss situation.

Breakevenvolumeis the amount of product that needs to be produced and sold to cover total costs of production.

Explanation of Solution

  $\begin{array}{c}\text{Break}\text{even}\text{point}=\frac{\text{2}\times \text{Fixed}\text{cost}}{\text{Selling}\text{price}-\text{Variable}\text{cost}}\\ =\frac{\$60000\times 2}{\$12-\$7}\\ =24,000\text{units}\end{array}$

Thus, the break-even volume with two shifts is $24,000 units.