Chapter 7.S, Problem 26P

a)

Summary Introduction

To determine: The break-even point in dollars per month.

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 with the total costs. The total profit at break-even point is 0.

Answer to Problem 26P

The break-even point in dollars per month is $7,584.83

Explanation of Solution

Given information:

	Selling Price (P)	Variable Cost (VC)	Volume (V)
Drinks	1.50	0.75	30,000
Meals	10.00	5.00	10,000
Desserts	2.50	1.00	10,000
Sandwiches	6.25	3.25	20,000

$\begin{array}{c}\text{Fixed cost}=\text{Rent, utilities cost}+\text{Entertainment cost}\\ =\text{\$1,800}+\text{\$2,000}\\ =\text{\$3,800 / month}\end{array}$

Formula to calculate Revenue:

$\text{Revenue}=\text{Selling price}\times \text{Volume}$

Calculation of Revenue:

The revenue is calculated by multiplying the selling price with volume.

Drinks:

$\begin{array}{c}\text{Revenue}=\$\text{1}\text{.50}\times \text{30,000}\\ =\text{\$45,000}\end{array}$

Meals:

$\begin{array}{c}\text{Revenue}=\$\text{10}\times 1\text{0,000}\\ =\text{\$100,000}\end{array}$

Desserts:

$\begin{array}{c}\text{Revenue}=\$2.\text{50}\times 1\text{0,000}\\ =\text{\$25,000}\end{array}$

Lunch:

$\begin{array}{c}\text{Revenue}=\$6.\text{25}\times 2\text{0,000}\\ =\text{\$125,000}\end{array}$

Formula to calculate total revenue:

$\text{Total revenue}={\displaystyle \sum \text{Individual revenue}}$

Calculation of total revenue:

The total revenue is calculated by summing all the individual revenue.

$\begin{array}{c}\text{Total revenue}=\$45,000+\$100,000+\$25,000+\$125,000\\ =\$295,000\end{array}$

Formula to calculate percent of total revenue:

$\text{Percent of total revenue}=\frac{\text{Individual revenue}}{\text{Total revenue}}$

Calculation of percent of total revenue:

The percent of total revenue is calculated by dividing the individual revenue with the total revenue.

Drinks:

$\begin{array}{c}\text{Percent of total revenue}=\frac{\text{\$45,000}}{\text{\$295,000}}\\ =0.153\end{array}$

Meals:

$\begin{array}{c}\text{Percent of total revenue}=\frac{\text{\$100,000}}{\text{\$295,000}}\\ =0.339\end{array}$

Desserts:

$\begin{array}{c}\text{Percent of total revenue}=\frac{\text{\$25,000}}{\text{\$295,000}}\\ =0.085\end{array}$

Sandwiches:

$\begin{array}{c}\text{Percent of total revenue}=\frac{\text{\$125,000}}{\text{\$295,000}}\\ =0.423\end{array}$

Formula to calculate total percent of total revenue:

$\text{Total of percent of total revenue}={\displaystyle \sum \text{Percent of total revenue}}$

Calculation of Total percent of total revenue:

The total of percent of total revenue is calculated by summing all the individual percent of total revenue.

$\begin{array}{c}\text{Total of percent of total revenue}=0.153+0.339+0.085+0.423\\ =1.000\end{array}$

Calculation of $\frac{VC}{P}$ :

The value is calculated by dividing the variable cost by selling price.

Drinks:

$\begin{array}{c}\text{Drinks}=\frac{0.75}{1.50}\\ =0.50\end{array}$

Meals:

$\begin{array}{c}\text{Meals}=\frac{5.00}{10.00}\\ =0.50\end{array}$

Desserts:

$\begin{array}{c}\text{Desserts}=\frac{1.00}{2.50}\\ =0.40\end{array}$

Sandwiches:

$\begin{array}{c}\text{Sandwiches}=\frac{3.25}{6.25}\\ =0.52\end{array}$

Calculation of $1-\frac{VC}{P}$ :

The value is calculated by subtracting 1 with $\frac{VC}{P}$.

Drinks:

$\begin{array}{c}\text{Drinks}=1-0.50\\ =0.50\end{array}$

Meals:

$\begin{array}{c}\text{Meals}=1-0.50\\ =0.50\end{array}$

Desserts:

$\begin{array}{c}\text{Desserts}=1-0.40\\ =0.60\end{array}$

Sandwiches:

$\begin{array}{c}\text{Drinks}=1-0.52\\ =0.48\end{array}$

Calculation of $1-\frac{VC}{P}\times Percentoftotalrevenue$:

The value is calculated multiplying the percent of total revenue with the value of $1-\frac{VC}{P}$.

Drinks:

$\begin{array}{c}\text{Drinks}=0.50\times 0.153\\ =0.077\end{array}$

Meals:

$\begin{array}{c}\text{Meals}=0.50\times 0.339\\ =0.170\end{array}$

Desserts:

$\begin{array}{c}\text{Desserts}=0.60\times 0.085\\ =0.051\end{array}$

Sandwiches:

$\begin{array}{c}\text{Sandwichess}=0.48\times 0.423\\ =0.203\end{array}$

Formula to calculate total value of $1-\frac{VC}{P}\times Percentoftotalrevenue$:

$\text{Total=}{\displaystyle \sum \text{1}-\frac{\text{VC}}{\text{P}}\times \text{Percent of total revenue}}$

Calculation of total value of $1-\frac{VC}{P}\times Percentoftotalrevenue$:

The value is calculated by summing all the individual values of $1-\frac{VC}{P}\times Percentoftotalrevenue$.

$\begin{array}{c}\text{Total}=0.077+0.170+0.051+0.203\\ =0.501\end{array}$

Formula to calculate break-even point (BEP) in dollars:

${\text{BEP}}_{\$}=\frac{\text{Fixed cost}}{{\displaystyle \sum \text{1}-\frac{\text{VC}}{\text{P}}\times \text{Percent of total revenue}}}$

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

The Break-even point is calculated by dividing the fixed cost with the value of ${\displaystyle \sum \text{1}-\frac{\text{VC}}{\text{P}}\times \text{Percent of total revenue}}$.

$\begin{array}{c}{\text{BEP}}_{\$}=\frac{3,800}{0.501}\\ =\$7,584.83\end{array}$

Hence, the Break-even point (BEP) in dollarsis$7,584.83.

b)

Summary Introduction

To determine: The break-even units per day if it is open for 30 days a month.

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 with the total costs. The total profit at break-even point is 0.

Answer to Problem 26P

The break-even units per day if it is open for 30 days a month is 9 / day.

Explanation of Solution

Given information:

	Selling Price (P)	Variable Cost (VC)	Volume (V)
Drinks	1.50	0.75	30,000
Meals	10.00	5.00	10,000
Desserts	2.50	1.00	10,000
Sandwiches	6.25	3.25	20,000

$\begin{array}{c}\text{Fixed cost}=\text{Rent, utilities cost}+\text{Entertainment cost}\\ =\text{\$1,800}+\text{\$2,000}\\ =\text{\$3,800 / month}\end{array}$

Formula to calculate Revenue:

$\text{Revenue}=\text{Selling price}\times \text{Volume}$

Calculation of Revenue:

The revenue is calculated by multiplying the selling price with volume.

Drinks:

$\begin{array}{c}\text{Revenue}=\$\text{1}\text{.50}\times \text{30,000}\\ =\text{\$45,000}\end{array}$

Meals:

$\begin{array}{c}\text{Revenue}=\$\text{10}\times 1\text{0,000}\\ =\text{\$100,000}\end{array}$

Desserts:

$\begin{array}{c}\text{Revenue}=\$2.\text{50}\times 1\text{0,000}\\ =\text{\$25,000}\end{array}$

Lunch:

$\begin{array}{c}\text{Revenue}=\$6.\text{25}\times 2\text{0,000}\\ =\text{\$125,000}\end{array}$

Formula to calculate total revenue:

$\text{Total revenue}={\displaystyle \sum \text{Individual revenue}}$

Calculation of total revenue:

The total revenue is calculated by summing all the individual revenue.

$\begin{array}{c}\text{Total revenue}=\$45,000+\$100,000+\$25,000+\$125,000\\ =\$295,000\end{array}$

Formula to calculate percent of total revenue:

$\text{Percent of total revenue}=\frac{\text{Individual revenue}}{\text{Total revenue}}$

Calculation of percent of total revenue:

The percent of total revenue is calculated by dividing the individual revenue with the total revenue.

Drinks:

$\begin{array}{c}\text{Percent of total revenue}=\frac{\text{\$45,000}}{\text{\$295,000}}\\ =0.153\end{array}$

Meals:

$\begin{array}{c}\text{Percent of total revenue}=\frac{\text{\$100,000}}{\text{\$295,000}}\\ =0.339\end{array}$

Desserts:

$\begin{array}{c}\text{Percent of total revenue}=\frac{\text{\$25,000}}{\text{\$295,000}}\\ =0.085\end{array}$

Sandwiches:

$\begin{array}{c}\text{Percent of total revenue}=\frac{\text{\$125,000}}{\text{\$295,000}}\\ =0.423\end{array}$

Formula to calculate total percent of total revenue:

$\text{Total of percent of total revenue}={\displaystyle \sum \text{Percent of total revenue}}$

Calculation of Total percent of total revenue:

The total of percent of total revenue is calculated by summing all the individual percent of total revenue.

$\begin{array}{c}\text{Total of percent of total revenue}=0.153+0.339+0.085+0.423\\ =1.000\end{array}$

Calculation of $\frac{VC}{P}$ :

The value is calculated by dividing the variable cost by selling price.

Drinks:

$\begin{array}{c}\text{Drinks}=\frac{0.75}{1.50}\\ =0.50\end{array}$

Meals:

$\begin{array}{c}\text{Meals}=\frac{5.00}{10.00}\\ =0.50\end{array}$

Desserts:

$\begin{array}{c}\text{Desserts}=\frac{1.00}{2.50}\\ =0.40\end{array}$

Sandwiches:

$\begin{array}{c}\text{Sandwiches}=\frac{3.25}{6.25}\\ =0.52\end{array}$

Calculation of $1-\frac{VC}{P}$ :

The value is calculated by subtracting 1 with $\frac{VC}{P}$.

Drinks:

$\begin{array}{c}\text{Drinks}=1-0.50\\ =0.50\end{array}$

Meals:

$\begin{array}{c}\text{Meals}=1-0.50\\ =0.50\end{array}$

Desserts:

$\begin{array}{c}\text{Desserts}=1-0.40\\ =0.60\end{array}$

Sandwiches:

$\begin{array}{c}\text{Drinks}=1-0.52\\ =0.48\end{array}$

Calculation of $1-\frac{VC}{P}\times Percentoftotalrevenue$:

The value is calculated multiplying the percent of total revenue with the value of $1-\frac{VC}{P}$.

Drinks:

$\begin{array}{c}\text{Drinks}=0.50\times 0.153\\ =0.077\end{array}$

Meals:

$\begin{array}{c}\text{Meals}=0.50\times 0.339\\ =0.170\end{array}$

Desserts:

$\begin{array}{c}\text{Desserts}=0.60\times 0.085\\ =0.051\end{array}$

Sandwiches:

$\begin{array}{c}\text{Sandwichess}=0.48\times 0.423\\ =0.203\end{array}$

Formula to calculate total value of $1-\frac{VC}{P}\times Percentoftotalrevenue$:

$\text{Total=}{\displaystyle \sum \text{1}-\frac{\text{VC}}{\text{P}}\times \text{Percent of total revenue}}$

Calculation of total value of $1-\frac{VC}{P}\times Percentoftotalrevenue$:

The value is calculated by summing all the individual values of $1-\frac{VC}{P}\times Percentoftotalrevenue$.

$\begin{array}{c}\text{Total}=0.077+0.170+0.051+0.203\\ =0.501\end{array}$

Formula to calculate break-even point (BEP) in dollars:

${\text{BEP}}_{\$}=\frac{\text{Fixed cost}}{{\displaystyle \sum \text{1}-\frac{\text{VC}}{\text{P}}\times \text{Percent of total revenue}}}$

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

The Break-even point is calculated by dividing the fixed cost with the value of ${\displaystyle \sum \text{1}-\frac{\text{VC}}{\text{P}}\times \text{Percent of total revenue}}$.

$\begin{array}{c}{\text{BEP}}_{\$}=\frac{\$3,800}{0.501}\\ =\$7,584.83\end{array}$

The Break-even point (BEP) in dollars is $7,584.83.

Formula to calculate Dollar volume:

$\text{Dollar volume}=\text{Percent of total revenu}e\times {\text{BEP}}_{\$}$

Calculation of dollar volume:

The dollar volume is calculated by multiplying percent of total revenue with the BEP in dollars.

Drinks:

$\begin{array}{c}\text{Dollar volume}=0.153\times \$7,584.83\\ =\$1,160.48\end{array}$

Meals:

$\begin{array}{c}\text{Dollar volume}=0.339\times \$7,584.83\\ =\$2,571.26\end{array}$

Desserts:

$\begin{array}{c}\text{Dollar volume}=0.085\times \$7,584.83\\ =\$644.71\end{array}$

Lunch:

$\begin{array}{c}\text{Dollar volume}=0.423\times \$7,584.83\\ =\$3,208.38\end{array}$

Formula to calculate BEP units per month:

$\text{BEP}=\frac{\text{Dollar volume}}{\text{Selling}\text{price}}$

Drinks:

$\begin{array}{c}\text{BEP}=\frac{\$1,160.48}{\$1.50}\\ =774\text{ units / month}\end{array}$

Meals:

$\begin{array}{c}\text{BEP}=\frac{\$2,571.26}{\$10.00}\\ =258\text{ units / month}\end{array}$

Desserts:

$\begin{array}{c}\text{BEP}=\frac{\$644.71}{\$2.50}\\ =258\text{ units / month}\end{array}$

Sandwiches:

$\begin{array}{c}\text{BEP}=\frac{\$3,208.28}{\$6.25}\\ =514\text{ units / month}\end{array}$

Formula to calculate BEP per day:

$BE{P}_{day}=\frac{BEP/month}{30days/month}$

Drinks:

$\begin{array}{c}{\text{BEP}}_{\text{day}}=\frac{774}{30}\\ =25.8\\ =26\end{array}$

Meals:

$\begin{array}{c}{\text{BEP}}_{\text{day}}=\frac{258}{30}\\ =8.6\\ =9\end{array}$

Desserts:

$\begin{array}{c}{\text{BEP}}_{\text{day}}=\frac{258}{30}\\ =8.6\\ =9\end{array}$

Sandwiches:

$\begin{array}{c}{\text{BEP}}_{\text{day}}=\frac{514}{30}\\ =17.13\\ =18\end{array}$

Hence, the BEP unit per day is9 units.