Chapter 7.S, Problem 25P

a)

Summary Introduction

To determine: The break-even point quantity for the manual process.

Introduction:

Break-even point (BEP):

The break-even point is measured in units or in sales term to identify the point in a business which is required to cover the total investment costs. The total profit at break-even point is zero.

Answer to Problem 25P

The break-even point quantity for the manual process is 50,000 bags.

Explanation of Solution

Given information:

Manual process:

Fixed costs= $37,500 / month

Variable costs = $1.75 / bag

Selling price = $2.50 / bag

Mechanized process:

Fixed cost = $75,000 / month

Variable cost = $1.25 / bag

Selling price = $2.50 / bag

Formula to calculate Break-even point (BEP) in units:

${\text{BEP}}_{\text{bags}}=\frac{\text{Fixed cost}}{\text{Selling price}-\text{Variable cost}}$

Calculation of Break-even point (BEP) in units:

The Break-even point is calculated by dividing the fixed cost with the difference of selling price and variable cost.

$\begin{array}{c}{\text{BEP}}_{bags}=\frac{\text{\$37,500}}{\text{\$2}\text{.50}-\text{\$1}\text{.75}}\\ =\frac{\text{\$37,500}}{\text{\$0}\text{.75}}\\ =50\text{,000 bags}\end{array}$

Hence, the Break-even point (BEP) in units is 50,000 bags.

b)

Summary Introduction

To determine: The revenue for the manual process at break-even point quantity.

Introduction:

Break-even point (BEP):

The break-even point is measured in units or in sales term to identify the point in a business which is required to cover the total investment costs. The total profit at break-even point is zero.

Answer to Problem 25P

The revenue for the manual process at break-even point quantity is $125,000.

Explanation of Solution

Given information:

Manual process:

Fixed costs = $37,500 / month

Variable costs = $1.75 / bag

Selling price = $2.50 / bag

Mechanized process:

Fixed cost = $75,000 / month

Variable cost = $1.25 / bag

Selling price = $2.50 / bag

Formula to calculate Revenue for the manual process:

${\text{BEP}}_{\text{\$}}=\frac{\text{Fixed cost}}{\text{1}-\frac{\text{Variable cost}}{Selling\text{ price}}}$

Calculation of Revenue

The revenue is calculated by dividing the fixed cost with the value obtained by dividing the resultant value obtained from dividing the difference between the selling price and variable cost divided by the selling price.

$\begin{array}{c}BE{P}_{\$}=\frac{\$37,500}{1-\frac{\$1.75}{\$2.50}}\\ =\frac{\$37,500}{\frac{\$2.50-\$1.75}{\$2.50}}\end{array}$

$\begin{array}{c}=\frac{\$37,500}{\frac{\$0.75}{\$2.50}}\\ =\frac{\$37,500}{\$0.3}\\ =\$125,000\end{array}$

Hence, the revenue for the manual process at break-even point quantity is $125,000.

c)

Summary Introduction

To determine: The break-even point quantity for the mechanized process.

Answer to Problem 25P

The break-even point quantity for the mechanized process is 60,000 bags.

Explanation of Solution

Given information:

Manual process:

Fixed costs = $37,500 / month

Variable costs = $1.75 / bag

Selling price = $2.50 / bag

Mechanized process:

Fixed cost = $75,000 / month

Variable cost = $1.25 / bag

Selling price = $2.50 / bag

Formula to calculate Break-even point (BEP) in units:

${\text{BEP}}_{\text{bags}}=\frac{\text{Fixed cost}}{\text{Selling price}-\text{Variable cost}}$

Calculation of Break-even point (BEP) in units:

The Break-even point is calculated by dividing the fixed cost with the difference of selling price and variable cost.

$\begin{array}{c}{\text{BEP}}_{bags}=\frac{\text{\$75,000}}{\text{\$2}\text{.50}-\$\text{1}\text{.25}}\\ =\frac{\text{\$75,000}}{\text{\$1}\text{.25}}\\ =60\text{,000 bags}\end{array}$

Hence, the Break-even point (BEP) in units is 60,000 bags.

d)

Summary Introduction

To determine: The revenue for the mechanized process at break-even point quantity.

Answer to Problem 25P

The revenue for the mechanized process at break-even point quantity is $150,000.

Explanation of Solution

Given information:

Manual process:

Fixed costs = $37,500 / month

Variable costs = $1.75 / bag

Selling price = $2.50 / bag

Mechanized process:

Fixed cost = $75,000 / month

Variable cost = $1.25 / bag

Selling price = $2.50 / bag

Formula to calculate Revenue for the manual process:

${\text{BEP}}_{\text{\$}}=\frac{\text{Fixed cost}}{\text{1}-\frac{\text{Variable cost}}{Selling\text{ price}}}$

Calculation of Revenue

The revenue is calculated by dividing the fixed cost with the value obtained by dividing the resultant value obtained from dividing the difference between the selling price and variable cost divided by the selling price.

$\begin{array}{c}BE{P}_{\$}=\frac{\$75,000}{1-\frac{\$1.25}{\$2.50}}\\ =\frac{\$75,000}{\frac{\$2.50-\$1.25}{\$2.50}}\end{array}$

$\begin{array}{c}=\frac{\$75,000}{\frac{\$1.25}{\$2.50}}\\ =\frac{\$75,000}{\$0.5}\\ =\$150,000\end{array}$

Hence, the revenue for the manual process at break-even point quantity is $150,000.

e)

Summary Introduction

To determine: The monthly profit or loss for the manual process for the sale of 60,000 bags of lettuce per month.

Answer to Problem 25P

The monthly profit for the manual process for the sale of 60,000 bags of lettuce per month is $7,500.

Explanation of Solution

Given information:

Manual process:

Fixed costs = $37,500 / month

Variable costs = $1.75 / bag

Selling price = $2.50 / bag

Mechanized process:

Fixed cost = $75,000 / month

Variable cost = $1.25 / bag

Selling price = $2.50 / bag

Formula to calculate Profit or loss:

$\text{Profit}=\left(\begin{array}{l}\text{Number of bags of lettuce}\times \\ \text{Selling price}\end{array}\right)-\left(\begin{array}{l}\text{Number of bags of lettuce}\times \\ \text{Variable cost}\end{array}\right)-\text{Fixed cost}$

Calculation of profit or loss for manual process:

The profit is calculated by multiplying number of bags of lettuce with selling price and the resultant value is subtracted from the fixed cost and the value obtained by multiplying number of bags of lettuce and variable cost.

$\begin{array}{c}\text{Profit}=\left(\text{\$60,000}\times \$2.\text{50}\right)-\left(\text{\$60,000}\times \$1.\text{75}\right)-\$37\text{,500}\\ =\$150,000-\$105,000-\$37,500\\ =\$7,500\end{array}$

The monthly profit for the manual process for the sale of 60,000 bags of lettuce per month is $7,500.

f)

Summary Introduction

To determine: The monthly profit or loss for the mechanized process for the sale of 60,000 bags of lettuce per month.

Answer to Problem 25P

The monthly profit or lossfor the mechanized process for the sale of 60,000 bags of lettuce per month is $0which is the break-even point.

Explanation of Solution

Given information:

Manual process:

Fixed costs = $37,500 / month

Variable costs = $1.75 / bag

Selling price = $2.50 / bag

Mechanized process:

Fixed cost = $75,000 / month

Variable cost = $1.25 / bag

Selling price = $2.50 / bag

Formula to calculate Profit or loss:

$\text{Profit}=\left(\begin{array}{l}\text{Number of bags of lettuce}\times \\ \text{Selling price}\end{array}\right)-\left(\begin{array}{l}\text{Number of bags of lettuce}\times \\ \text{Variable cost}\end{array}\right)-\text{Fixed cost}$

Calculation of profit or loss for mechanized process:

The profit is calculated by multiplying number of bags of lettuce with selling price and the resultant value is subtracted from the fixed cost and the value obtained by multiplying number of bags of lettuce and variable cost.

$\begin{array}{c}\text{Profit}=\left(\text{\$60,000}\times \$2.\text{50}\right)-\left(\text{\$60,000}\times \$1.\text{25}\right)-\$75\text{,000}\\ =\$150,000-\$75,000-\$75,000\\ =\$0\end{array}$

Hence, the monthly profit or loss for the mechanized process for the sale of 60,000 bags of lettuce per month is $0 which is the break-even point.

g)

Summary Introduction

To determine: The point at which both the process will yield the same amount.

Answer to Problem 25P

The point at which both the process will yield the same amount is 75,000 bags.

Explanation of Solution

Given information:

Manual process:

Fixed costs = $37,500 / month

Variable costs = $1.75 / bag

Selling price = $2.50 / bag

Mechanized process:

Fixed cost = $75,000 / month

Variable cost = $1.25 / bag

Selling price = $2.50 / bag

$\begin{array}{l}\text{Let }{F}_A\text{ be the fixed cost manual process}\text{.}\\ {\text{Let V}}_{\text{A}}\text{ be the variable cost of manual process}\text{.}\\ {\text{Let F}}_{\text{B}}\text{ be the fixed cost for mechanized process}\text{.}\end{array}$

$\begin{array}{l}{\text{Let V}}_{\text{B}}\text{ be the variable cost for mechanized process}\text{. }\\ \text{Let x be the volume of bags of lettuces}\text{.}\\ \text{Let S be the selling price of bag of lettuces}\text{.}\end{array}$

Formation of equation 1 for manual process:

$\left(S-V_A\right)x-F_A$ (1)

Formation of equation 2 for mechanized process:

$\left(S-V_B\right)x-F_B$ (2)

Calculation of the point at which both process yields the same amount:

The point is calculated by substituting all the known values in equation (1) and (2) and equating each other.

$\begin{array}{c}\left(S-V_A\right)x-F_A=\left(S-V_B\right)x-F_B\\ \left(\$2.50-\$1.75\right)x-\$37,500=\left(\$2.50-\$1.25\right)x-\$75,000\\ 0.75x-\$37,500=1.25x-\$75,000\\ 0.75x-1.25x=-\$75,000+\$37,500\end{array}$

$\begin{array}{c}-0.50x=-37,500\\ x=\frac{-37,500}{-0.50}\\ =75,000bags\end{array}$

Hence, the point at which both the process will yield the same amount is 75,000 bags.

h)

Summary Introduction

To determine: The range of demand at which the manual process will be preferred over the mechanized process and the range of demand at which the mechanized will be preferred over the manual process.

Introduction:

Indifference point:

The indifference point in a business is a point where two different types of alternatives will not have any difference in the output they yield.

Answer to Problem 25P

The manual process will be preferred over the mechanized process for the volume below 75,000 bags. The mechanized process will be preferred over the manual process for the volume above 75,000 bags.

Figure for showing the range at which one process will be better than the other:

Explanation of Solution

Given information:

Manual process:

Fixed costs = $37,500 / month

Variable costs = $1.75 / bag

Selling price = $2.50 / bag

Mechanized process:

Fixed cost = $75,000 / month

Variable cost = $1.25 / bag

Selling price = $2.50 / bag

$\begin{array}{l}\text{Let }{F}_A\text{ be the fixed cost manual process}\text{.}\\ {\text{Let V}}_{\text{A}}\text{ be the variable cost of manual process}\text{.}\\ {\text{Let F}}_{\text{B}}\text{ be the fixed cost for mechanized process}\text{.}\end{array}$

$\begin{array}{l}{\text{Let V}}_{\text{B}}\text{ be the variable cost for mechanized process}\text{. }\\ \text{Let x be the volume of bags of lettuces}\text{.}\\ \text{Let S be the selling price of bag of lettuces}\text{.}\end{array}$

Formation of equation 1 for manual process:

$\left(S-V_A\right)x-F_A$ (1)

Formation of equation 2 for mechanized process:

$\left(S-V_B\right)x-F_B$ (2)

Calculation of the point at which both process yields the same amount:

The point is calculated by substituting all the known values in equation (1) and (2) and equating each other.

$\begin{array}{c}\left(S-V_A\right)x-F_A=\left(S-V_B\right)x-F_B\\ \left(\$2.50-\$1.75\right)x-\$37,500=\left(\$2.50-\$1.25\right)x-\$75,000\\ 0.75x-37,500=1.25x-\$75,000\\ 0.75x-1.25x=-\$75,000+\$37,500\end{array}$

$\begin{array}{c}-0.50x=-\$37,500\\ x=\frac{-\$37,500}{-\$0.50}\\ =75,000bags\end{array}$

The fixed costs of both the processes are plotted as shown in the graph.  The intersection point in the graph is the point where both process will have no advantage over the other. It is also known as the indifference point. The indifference point is 75, 000 bags.

Hence, the manual process will be preferred over the mechanized process for the volume below 75,000 bags. The mechanized process will be preferred over the manual process for the volume above 75,000 bags.