Chapter 5, Problem 12P

Healthy Foods Inc. sells 50-pound bags of grapes to the military for $\text{\$10}$ a bag. The fixed costs of this operation are $\text{\$80,000}$ , while the variable costs of grapes are $\text{\$0}\text{.10}$ per pound.

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

b. Calculate the profit or loss on 12,000 bags and on 25,000 bags.

c. What is the degree of operating leverage at 20,000 bags and at 25,000 bags? Why does the degree of operating leverage change as the quantity sold increases?

d. If Healthy Foods has an annual interest expense of $\text{\$10,000}$ , calculate the degree of financial leverage at both 20,000 and 25,000 bags.

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

Summary Introduction

To calculate: The break-even point (BEP) of Healthy Foods Inc.

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 12P

The BEP of Healthy Foods Inc. is 16,000 bags.

Explanation of Solution

Calculation of BEP of Healthy Foods Inc.:

$\begin{array}{c}\text{BEP}=\frac{\text{Fixed cost}}{\text{Price of sale per bag}-\left(\text{Variable cost per unit}\times \text{Number of bags sold}\right)}\\ =\frac{\$80,000}{\$10-(\$0.10\times 50)}\\ =\frac{\$80,000}{\$5}\\ =16,000\text{ bags}\end{array}$

Summary Introduction

To calculate: The profit or loss for Healthy Foods Inc. on 12,000 as well as 25,000 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 12P

Calculation of profit or loss on 12,000 bags and 25,000 bags for Healthy Foods Inc:

Explanation of Solution

The formulae used for the computation of profit or loss of 12,000 bags and 25,000 bags:

Summary Introduction

To calculate: The DOL for 20,000 and 25,000 bags of Healthy Foods Inc. and also explain the reason behind the change of DOL with the increase in the 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 12P

The DOL for Healthy Foods Inc. for 20,000 bags is 5 times and for 25,000 bags is 2.78 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 20,000 bags:

$\begin{array}{c}\text{DOL at }20,000\text{ bags}=\frac{\left[\text{Quantity}\times (\text{Price}-\text{Variable Cost})\right]}{\left[\text{Quantity}\times (\text{Price}-\text{Variable Cost})\right]-\text{Fixed Cost}}\\ =\frac{\left[20,000\times (\$10-\$5)\right]}{\left[20,000\times (\$10-\$5)\right]-\$80,000}\\ =\frac{\$100,000}{\$20,000}\\ =5\text{ times}\end{array}$

Calculation of DOL for 25,000 bags:

$\begin{array}{c}\text{DOL at }25,000\text{ bags}=\frac{\left[\text{Quantity}\times (\text{Price}-\text{Variable Cost})\right]}{\left[\text{Quantity}\times (\text{Price}-\text{Variable Cost})\right]-\text{Fixed Cost}}\\ =\frac{\left[25,000\times (\$10-\$5)\right]}{\left[25,000\times (\$10-\$5)\right]-\$80,000}\\ =\frac{\$125,000}{\$45,000}\\ =2.78\text{ times}\end{array}$

Summary Introduction

To calculate: The DFL of Healthy Foods Inc.for 20,000 bags as well as 25,000 bags.

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 12P

DFL for the company Healthy Foods Inc. for 20,000 bags is 2 times and for 25,000 bags is 1.29 times.

Explanation of Solution

Calculation of DFL for 20,000 bags:

$\begin{array}{c}\text{DFL of }20,000\text{ bags}=\frac{\text{EBIT}}{\text{EBIT}-\text{Interest}}\\ =\frac{\$20,000}{\$20,000-\$10,000}\\ =\frac{\$20,000}{\$10,000}\\ =2\text{ times}\end{array}$

Calculation of DFL for 25,000 bags:

$\begin{array}{c}\text{DFL at }25,000\text{ bags}=\frac{\text{EBIT}}{\text{EBIT}-\text{Interest}}\\ =\frac{\$45,000}{\$45,000-\$10,000}\\ =\frac{\$45,000}{\$35,000}\\ =1.29\text{ times}\end{array}$

Working note:

Calculation of EBIT on 20,000 bags:

$\begin{array}{c}\text{EBIT at }20,000\text{ bags}=\text{Sales}-\text{Variable Cost}-\text{Fixed Cost}\\ =\$200,000-\$100,000-\$80,000\\ =\$20,000\end{array}$

Calculation of EBIT on 25,000 bags:

$\begin{array}{c}\text{EBIT at }25,000\text{ bags}=\text{Sales}-\text{Variable Cost}-\text{Fixed Cost}\\ =\$250,000-\$125,000-\$80,000\\ =\$45,000\end{array}$

Summary Introduction

To calculate: The DCL of Healthy foods Inc. at 20,000 and 25,000 bags, respectively.

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 12P

DCL for the company Healthy Foods Inc. for 20,000 bags is 10 times and for 25,000 bags is 3.57 times.

Explanation of Solution

Explanation:

Calculation of DCL on 20,000 bags:

$\begin{array}{c}\text{DCL at 20,000 bags}=\frac{\left[\text{Quantity}\times (\text{Price}-\text{Variable Cost})\right]}{\left[\text{Quantity}\times (\text{Price}-\text{Variable Cost})\right]-\text{Fixed Cost}-\text{Interest}}\\ =\frac{\left[20,000\times (\$10-\$5)\right]}{\left[20,000\times (\$10-\$5)\right]-\$80,000-\$10,000}\\ =\frac{\$100,000}{\$10,000}\\ =10\text{ times}\end{array}$

Calculation of DCL on 25,000 bags:

$\begin{array}{c}\text{DCL at 25,000 bags}=\frac{\left[\text{Quantity}\times (\text{Price}-\text{Variable Cost})\right]}{\left[\text{Quantity}\times (\text{Price}-\text{Variable Cost})\right]-\text{Fixed Cost}-\text{Interest}}\\ =\frac{\left[25,000\times (\$10-\$5)\right]}{\left[25,000\times (\$10-\$5)\right]-\$80,000-\$10,000}\\ =\frac{\$125,000}{\$35,000}\\ =3.57\text{ units}\end{array}$