Chapter 7.S, Problem 20P

a)

Summary Introduction

To determine: The break-even point of each oven given.

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 20P

The break-even point of oven type A is 1,667 pizzas. The break-even point of oven type B is 2,353 pizzas.

Explanation of Solution

Given information:

Oven type A:

Number of pizzas = 20 / hour

Fixed cost = $20,000

Variable cost = $2.00 / pizza

Selling price= $14.00/ pizza

Oven type B:

Number of pizzas = 40 / hour

Fixed cost = $30,000

Variable cost = $1.25 / pizza

Selling price = $14.00 / pizza

Formula to calculate Break-even point (BEP):

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

Calculation of Break-even point (BEP) of oven type A:

The break-even cost of an oven is calculated by finding out the number of pizzas that an oven can cook.

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

$\begin{array}{c}{\text{BEP}}_{\text{A}}=\frac{\text{\$20,000}}{\text{\$14}-\text{\$2}\text{.00}}\\ =\frac{\text{\$20,000}}{\$12}\\ =1666.67or1\text{,667 pizzas}\end{array}$

Hence, the Break-even point (BEP) for oven type A is 1,667 pizzas.

Calculation of Break-even point (BEP) of oven type B:

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

$\begin{array}{c}{\text{BEP}}_B=\frac{\text{\$30,000}}{\text{\$14}-\$\text{1}\text{.25}}\\ =\frac{\text{\$30,000}}{\$12.75}\\ =\$2,352.94\text{ or }2\text{,353 pizzas}\end{array}$

Hence, the Break-even point (BEP) for oven type B is 2,353 pizzas.

b)

Summary Introduction

To determine: The oven that need to be purchased if the owner is expecting to sell 9,000 pizzas.

Answer to Problem 20P

The oven that needs to be purchased if the owner is expecting to sell 9,000 pizzas is oven type A.

Explanation of Solution

Given information:

Oven type A:

Number of pizzas = 20 / hour

Fixed cost = $20,000

Variable cost = $2.00 / pizza

Selling price = $14.00 / pizza

Oven type B:

Number of pizzas = 40 / hour

Fixed cost = $30,000

Variable cost = $1.25 / pizza

Selling price = $14.00 / pizza

Formula to calculate Profit:

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

Calculation of profit for oven type A:

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

$\begin{array}{c}\text{Profit}=\left(\text{9,000}\times \text{14}\text{.00}\right)-\left(\text{9,000}\times \text{2}\text{.00}\right)-\text{20,000}\\ =126,000-18,000-20,000\\ =88,000\end{array}$

The profit for oven type A is $88,000.

Calculation of profit for oven type B:

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

$\begin{array}{c}\text{Profit}=\left(\text{\$9,000}\times \$\text{14}\text{.00}\right)-\left(\text{\$9,000}\times \$1.\text{25}\right)-\$3\text{0,000}\\ =\$126,000-\$11,250-\$30,000\\ =\$84,750\end{array}$

The profit for oven type B is $84,750.

The profit of oven type A is more than oven type B. (88,000 > 84,750)

Hence, the owner must purchase type A oven.

c)

Summary Introduction

To determine: The oven that need to be purchased if the owner is expecting to sell 12,000 pizzas.

Answer to Problem 20P

The oven that needs to be purchased if the owner is expecting to sell 12,000 pizzas is oven type A.

Explanation of Solution

Given information:

Oven type A:

Number of pizzas = 20 / hour

Fixed cost = $20,000

Variable cost = $2.00 / pizza

Selling price = $14.00 / pizza

Oven type B:

Number of pizzas = 40 / hour

Fixed cost = $30,000

Variable cost = $1.25 / pizza

Selling price = $14.00 / pizza

Formula to calculate Profit:

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

Calculation profit for oven type A:

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

$\begin{array}{c}\text{Profit}=\left(\text{\$12,000}\times \$\text{14}\text{.00}\right)-\left(\text{\$12,000}\times \$\text{2}\text{.00}\right)-\$\text{20,000}\\ =\$168,000-\$24,000-\$20,000\\ =\$124,000\end{array}$

The profit for oven type A is $124,000.

Calculation profit for oven type B:

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

$\begin{array}{c}\text{Profit}=\left(\text{\$12,000}\times \$\text{14}\text{.00}\right)-\left(\text{\$12,000}\times \$1.\text{25}\right)-\$3\text{0,000}\\ =\$168,000-\$15,000-\$30,000\\ =\$123,000\end{array}$

The profit for oven type B is $123,000.

The profit of oven type A is more than oven type B. (124,000 > 123,000)

Hence, the owner must purchase type A oven.

d)

Summary Introduction

To determine: The volume of pizzas at which JE person must switch the ovens.

Answer to Problem 20P

The volume of pizzas at which JE person must switch the type of ovens is 13, 333 pizzas.

Explanation of Solution

Given information:

Oven type A:

Number of pizzas = 20 / hour

Fixed cost = $20,000

Variable cost = $2.00 / pizza

Selling price = $14.00 / pizza

Oven type B:

Number of pizzas = 40 / hour

Fixed cost = $30,000

Variable cost = $1.25 / pizza

Selling price = $14.00 / pizza

$\begin{array}{l}\text{Let }{F}_A\text{ be the fixed cost for oven type A}\text{.}\\ {\text{Let V}}_{\text{A}}\text{ be the variable cost for oven type A}\text{.}\\ {\text{Let F}}_{\text{B}}\text{ be the fixed cost for oven type B}\text{.}\end{array}$

$\begin{array}{l}{\text{Let V}}_{\text{B}}\text{ be the variable cost for oven type B}\text{. }\\ \text{Let x be the volume of pizzas}\text{.}\end{array}$

Formation of equation 1 for oven type A:

${\text{F}}_{\text{A}}+\left({\text{V}}_{\text{A}}\times \text{x}\right)$ (1)

Formation of equation 2 for oven type B:

${\text{F}}_B+\left({\text{V}}_B\times \text{x}\right)$ (2)

Calculation of volume of pizzas:

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

$\begin{array}{c}{F}_A+\left(V_A\times x\right)=F_B+\left(V_B\times x\right)\\ \$20,000+\left(\$2.00\times x\right)=\$30,000+\left(1.25\times x\right)\\ \$20,000+2x=\$30,000+1.25x\\ 2x-1.25x=\$30,000-\$20,000\end{array}$

$\begin{array}{c}0.75x=\$10,000\\ x=\frac{\$10,000}{0.75}\\ =13,333.33\text{ or }13,333pizzas\end{array}$

Hence, the volume of pizzas at which JE person must switch the type of ovens is 13, 333 pizzas.