Chapter 5, Problem 13P

United Snack Company sells 50-pound bags of peanuts to university dormitories for $\text{\$20}$ a bag. The fixed costs of this operation are $\text{\$176,250}$ , while the variable costs of peanuts are $\text{\$0}\text{.15}$ per pound.

a. What is the break-even point in bags?

b. Calculate the profit or loss on 7,000 bags and on 20,000 bags.

c. What is the degree of operating leverage at 19,000 bags and at 24,000 bags? Why does the degree of operating leverage change as the quantity sold increases?

d. If United Snack Company has an annual interest expense of $\text{\$15,000}$ , calculate the degree of financial leverage at both 19,000 and 24,000 bags.

e. What is the degree of combined leverage at both sales levels?

Summary Introduction

To calculate: The BEP of the bags for United Snack Company.

Introduction:

Break-even point (BEP):

It is a point of sale at which a company is in a no profit and no loss situation. The value of BEP is derived by dividing total fixed cost by the difference of revenue per unit and variable cost per unit.

Answer to Problem 13P

The BEP of United Snack company is 14,100 bags.

Explanation of Solution

Computation of the BEP of United Snack Company:

$\begin{array}{c}\text{BEP of bags}=\frac{\text{Fixed Cost}}{\text{Sale of one bag}-\left(\text{Variable Cost}\times \text{Number of bags sold}\right)}\\ =\frac{\$176,250}{\$20-\left(\$0.15\times 50\right)}\\ =\frac{\$176,250}{\$20-\$7.5}\\ =14,100\text{ bags}\end{array}$

Summary Introduction

To calculate: The profit or loss for United Snack Company at 7,000 bags as well as 20,000 bags.

Introduction:

Profit or Loss:

It refers to the gain or loss arising from the commercial transactions during a specified period of time and is used to assess the company’s financial performance.

Answer to Problem 13P

Calculation of the profit and loss on 7,000 bags and 20,000 bags for United Snack Company:

Explanation of Solution

The formulae used for the computation of profit or loss at 7,000 as well as 20,000 bags:

Working Notes:

Computation of variable cost per unit:

$\begin{array}{c}\text{Variable Cost per unit}=\text{Peanuts per pound}\times \text{Cost of Peanuts per pound}\\ \text{= 50}\times \$\text{0}\text{.15}\\ =\$7.5\end{array}$

Summary Introduction

To calculate: The DOL for both 19,000 and 24,000 bags of United Snack Company and also explain the reason behind the change of DOL with the increase in quantity sold.

Introduction:

Degree of Operating Leverage (DOL):

It is a multiple measurement ratio which determines the quantity of change in operating income of the company with the change in sales value.

Answer to Problem 13P

DOL of United Snack Company for 19,000 bags is 3.88 times and for 24,000 bags is 2.42 times.

The reason behind this change of DOL is that the leverage has gone down and is far away from BEP. Hence, we can say that the leverage has decreased and the organisation is operating on a greater profit base.

Explanation of Solution

Calculation of DOL for 19,000 bags:

$\begin{array}{c}\text{DOL of }19,000\text{ bags}=\frac{\left[\text{Quantity}\times \left(\text{Price}-\text{Variable Cost}\right)\right]}{\left[\text{Quantity}\times \left(\text{Price}-\text{Variable Cost}\right)\right]-\text{Fixed Cost}}\\ =\frac{\left[19,000\times \left(\$20-\$7.5\right)\right]}{\left[19,000\times \left(\$20-\$7.5\right)\right]-\$176,250}\\ =\frac{\$237,500}{\$61,250}\\ =3.88\text{ units}\end{array}$

Calculation of DOL for 24,000 bags:

$\begin{array}{c}\text{DOL of }24,000\text{ bags}=\frac{\left[\text{Quantity}\times \left(\text{Price}-\text{Variable Cost}\right)\right]}{\left[\text{Quantity}\times \left(\text{Price}-\text{Variable Cost}\right)\right]-\text{Fixed Cost}}\\ =\frac{\left[24,000\times \left(\$20-\$7.5\right)\right]}{\left[24,000\times \left(\$20-\$7.5\right)\right]-\$176,250}\\ =\frac{\left[24,000\times \$12.5\right]}{\left[24,000\times \$12.5\right]-\$176,250}\\ =2.42\text{ units}\end{array}$

Summary Introduction

To calculate: The DFL of United Snack Company.

Introduction:

Degree of financial leverage (DFL):

It is a multiple measurement ratio which determines the quantity of change in operating income of the company with the change in sales value.

Answer to Problem 13P

The DFL of United Snack Company for 19,000 bags is 1.32 times and for 24,000 bags is 1.53 units.

Explanation of Solution

Calculation of DFL for 19,000 bags:

$\begin{array}{c}\text{DFL at }19,000\text{ bags}=\frac{\text{Earning before Interest and Tax}}{\text{Earning before Interest and Tax}-\text{Interest}}\\ =\frac{\$61,250}{\$61,250-\$15,000}\\ =\frac{\$61,250}{\$46,250}\\ =1.32\text{ times}\end{array}$

Calculation of DFL for 24,000 bags:

$\begin{array}{c}\text{DFL at }24,000\text{ bags}=\frac{\text{Earning before Interest and Tax }}{\text{Earning before Interest and Tax}-\text{Interest}}\\ =\frac{\$123,750}{\$123,750-\$15,000}\\ =\frac{\$123,750}{\$108,750}\\ =1.14\text{ times}\end{array}$

Working Notes:

Calculation of EBIT of 19,000 bags:

$\begin{array}{c}\text{EBIT of 19,000 bags}=\text{Sales}-\text{Variable Cost}-\text{Fixed Cost}\\ =\$380,000-\$180,000-\$176,250\\ =\$61,250\end{array}$

Calculation of EBIT of 24,000 bags:

$\begin{array}{c}\text{EBIT of 24,000 bags}=\text{Sales}-\text{Variable Cost}-\text{Fixed Cost}\\ =\$480,000-\$180,000-\$176,250\\ =\$123,750\end{array}$

Summary Introduction

To calculate: The DCL of United Snack Company.

Introduction:

Degree of combined leverage (DCL):

It is a multiple measurement ratio which determines the quantity of change in operating income of the company with the change in sales value.

Answer to Problem 13P

The DCL of United Snack Company of 19,000 bags is 5.14 times and for 24,000 bags is 2.76 times.

Explanation of Solution

Computation of DCL of 19,000 bags:

$\begin{array}{c}\text{DCL at 19},000\text{ bags}=\frac{\left[\text{Quantity}\times \left(\text{Price}-\text{Variable Cost}\right)\right]}{\left[\text{Quantity}\times \left(\text{Price}-\text{Variable Cost}\right)\right]-\text{Fixed Cost}-\text{Interest}}\\ =\frac{\left[19,000\times \left(\$20-\$7.5\right)\right]}{\left[19,000\times \left(\$20-\$7.5\right)\right]-\$176,250-\$15,000}\\ =\frac{\$237,500}{\$237,500-\$176,250-\$15,000}\\ =5.14\text{ times}\text{.}\end{array}$

Computation of DCL of 24,000 bags:

$\begin{array}{c}\text{DCL at }24,000\text{ bags}=\frac{\left[\text{Quantity}\times \left(\text{Price}-\text{Variable Cost}\right)\right]}{\left[\text{Quantity}\times \left(\text{Price}-\text{Variable Cost}\right)\right]-\text{Fixed Cost}-\text{Interest}}\\ =\frac{\left[24,000\times \left(\$20-\$7.5\right)\right]}{\left[24,000\times \left(\$20-\$7.5\right)\right]-\$176,250-\$15,000}\\ =\frac{\$300,000}{\$300,000-\$176,250-\$15,000}\\ =2.76\text{ times}\text{.}\end{array}$