Chapter 7.S, Problem 27P

a)

Summary Introduction

To determine: The break-even volume per evening performance.

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 27P

The break-even volume per evening performance is $986.19

Explanation of Solution

Given information:

Item	Selling Price (P)	Variable Cost (VC)	% of Revenue
Soft Drink	$1.00	$0.65	25
Wine	$1.75	$0.95	25
Coffee	$1.00	$0.30	30
Candy	$1.00	$0.30	20

$\begin{array}{c}\text{Fixed cost}=\text{Labor cost}+\text{Booth rental cost for 5 booths at \$50}\\ =\$250+\left(5\times \$50\right)\\ =\$250+\$250\\ =\$500\end{array}$

$\begin{array}{c}\text{Variable cost }\%=100\%+10\%\\ =110\%\end{array}$

Formula to calculate Total variable cost (TVC):

$\text{TVC}=\text{Variable cost}\times \text{Variable cost \%}$

Calculation of Total variable cost (TVC):

The total variable cost is calculated by multiplying the variable cost with the variable cost percentage.

Soft Drinks:

$\begin{array}{c}\text{TVC}=0.65\times 110\%\\ =0.65\times \frac{110}{100}\\ =0.65\times 1.1\\ =0.715\end{array}$

Wine:

$\begin{array}{c}\text{TVC}=0.95\times 110\%\\ =0.95\times \frac{110}{100}\\ =0.95\times 1.1\\ =1.045\end{array}$

Coffee:

$\begin{array}{c}\text{TVC}=0.30\times 110\%\\ =0.30\times \frac{110}{100}\\ =0.30\times 1.1\\ =0.330\end{array}$

Candy:

$\begin{array}{c}\text{TVC}=0.30\times 110\%\\ =0.30\times \frac{110}{100}\\ =0.30\times 1.1\\ =0.330\end{array}$

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

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

Soft drinks:

$\begin{array}{c}\text{Soft drinks}=\frac{0.715}{1.00}\\ =0.715\end{array}$

Wine:

$\begin{array}{c}\text{Wine}=\frac{1.045}{1.75}\\ =0.597\end{array}$

Coffee:

$\begin{array}{c}\text{Coffee}=\frac{0.330}{1.00}\\ =0.330\end{array}$

Candy:

$\begin{array}{c}\text{Candy}=\frac{0.330}{1.00}\\ =0.330\end{array}$

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

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

Soft drinks:

$\begin{array}{c}\text{Soft drinks}=1-0.715\\ =0.285\end{array}$

Wine:

$\begin{array}{c}\text{Wine}=1-0.597\\ =0.403\end{array}$

Coffee:

$\begin{array}{c}\text{Coffee}=1-0.330\\ =0.670\end{array}$

Candy:

$\begin{array}{c}\text{Candy}=1-0.330\\ =0.670\end{array}$

Calculation of contribution of weighted revenue:

The contribution weighted revenue is calculated by multiplying the value of $1-\frac{TVC}{P}$ with the percent of revenue.

Soft drinks:

$\begin{array}{c}\text{Soft drinks}=0.285\times 0.25\\ =0.071\end{array}$

Wine:

$\begin{array}{c}\text{Wine}=0.403\times 0.30\\ =0.101\end{array}$

Coffee:

$\begin{array}{c}\text{Coffee}=0.670\times 0.30\\ =0.201\end{array}$

Sandwiches:

$\begin{array}{c}\text{Candy}=0.670\times 0.20\\ =0.134\end{array}$

Formula to calculate total of contribution weighted revenue:

$\text{Total of contribution weighted revenue}={\displaystyle \sum \text{Contribution weighted revenue}}$

Calculation of total contribution weighted revenue:

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

$\begin{array}{c}\text{Total contribution weighted revenue}=0.071+0.101+0.201+0.134\\ =0.507\end{array}$

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

${\text{BEP}}_{\$}=\frac{\text{Fixed cost}}{{\displaystyle \sum \text{Contribution weighted revenue}}}$

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

The Break-even point is calculated by dividing the fixed cost with the value of total contribution of weighted revenue.

$\begin{array}{c}{\text{BEP}}_{\$}=\frac{\$500}{0.507}\\ =\$986.19\end{array}$

Hence, the Break-even point (BEP) in dollarsis$986.19.

b)

Summary Introduction

To determine: The sales of wine each evening at the break-even point.

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 27P

The sales of wine each evening at the break-even point is 140.9 servings.

Explanation of Solution

Given information:

Item	Selling Price (P)	Variable Cost (VC)	% of Revenue
Soft Drink	$1.00	$0.65	25
Wine	$1.75	$0.95	25
Coffee	$1.00	$0.30	30
Candy	$1.00	$0.30	20

$\begin{array}{c}\text{Fixed cost}=\text{Labor cost}+\text{Booth rental cost for 5 booths at \$50}\\ =\$250+\left(5\times \$50\right)\\ =\$250+\$250\\ =\$500\end{array}$

$\begin{array}{c}\text{Variable cost }\%=100\%+10\%\\ =110\%\end{array}$

Formula to calculate Total variable cost (TVC):

$\text{TVC}=\text{Variable cost}\times \text{Variable cost \%}$

Calculation of Total variable cost (TVC):

The total variable cost is calculated by multiplying the variable cost with the variable cost percentage.

Soft Drinks:

$\begin{array}{c}\text{TVC}=0.65\times 110\%\\ =0.65\times \frac{110}{100}\\ =0.65\times 1.1\\ =0.715\end{array}$

Wine:

$\begin{array}{c}\text{TVC}=0.95\times 110\%\\ =0.95\times \frac{110}{100}\\ =0.95\times 1.1\\ =1.045\end{array}$

Coffee:

$\begin{array}{c}\text{TVC}=0.30\times 110\%\\ =0.30\times \frac{110}{100}\\ =0.30\times 1.1\\ =0.330\end{array}$

Candy:

$\begin{array}{c}\text{TVC}=0.30\times 110\%\\ =0.30\times \frac{110}{100}\\ =0.30\times 1.1\\ =0.330\end{array}$

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

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

Soft drinks:

$\begin{array}{c}\text{Soft drinks}=\frac{0.715}{1.00}\\ =0.715\end{array}$

Wine:

$\begin{array}{c}\text{Wine}=\frac{1.045}{1.75}\\ =0.597\end{array}$

Coffee:

$\begin{array}{c}\text{Coffee}=\frac{0.330}{1.00}\\ =0.330\end{array}$

Candy:

$\begin{array}{c}\text{Candy}=\frac{0.330}{1.00}\\ =0.330\end{array}$

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

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

Soft drinks:

$\begin{array}{c}\text{Soft drinks}=1-0.715\\ =0.285\end{array}$

Wine:

$\begin{array}{c}\text{Wine}=1-0.597\\ =0.403\end{array}$

Coffee:

$\begin{array}{c}\text{Coffee}=1-0.330\\ =0.670\end{array}$

Candy:

$\begin{array}{c}\text{Candy}=1-0.330\\ =0.670\end{array}$

Calculation of contribution of weighted revenue:

The contribution weighted revenue is calculated by multiplying the value of  $1-\frac{TVC}{P}$ with the percent of revenue.

Soft drinks:

$\begin{array}{c}\text{Soft drinks}=0.285\times 0.25\\ =0.071\end{array}$

Wine:

$\begin{array}{c}\text{Wine}=0.403\times 0.30\\ =0.101\end{array}$

Coffee:

$\begin{array}{c}\text{Coffee}=0.670\times 0.30\\ =0.201\end{array}$

Sandwiches:

$\begin{array}{c}\text{Candy}=0.670\times 0.20\\ =0.134\end{array}$

Formula to calculate total of contribution weighted revenue:

$\text{Total of contribution weighted revenue}={\displaystyle \sum \text{Contribution weighted revenue}}$

Calculation of total contribution weighted revenue:

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

$\begin{array}{c}\text{Total contribution weighted revenue}=0.071+0.101+0.201+0.134\\ =0.507\end{array}$

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

${\text{BEP}}_{\$}=\frac{\text{Fixed cost}}{{\displaystyle \sum \text{Contribution weighted revenue}}}$

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

The Break-even point is calculated by dividing the fixed cost with the value of total contribution of weighted revenue.

$\begin{array}{c}{\text{BEP}}_{\$}=\frac{\$500}{0.507}\\ =\$986.19\end{array}$

The Break-even point (BEP) in dollars is $986.19.

Formula to calculate number of wine servings at breakeven:

$\text{Number of wine servings}=\frac{\text{Break-even sales}\times \text{Percent of revenue}}{\text{Selling price of wine}}$

Calculation of number of wine servings at breakeven:

The number of wine servings is calculated by dividing the value obtained by multiplying the breakeven sales with percent of revenue with the selling price of wine.

$\begin{array}{c}\text{Number of wine servings}=\frac{\$986.19\times 0.25}{\$1.75}\\ =\frac{246.5475}{\$1.75}\\ =140.88\\ =140.9\text{ servings}\end{array}$

Hence, the number of wine servings each evening at break-even is 140.9 servings.