Chapter 17, Problem 27PS

Summary Introduction

(a)

To compute:

The percentage decline in sales, if the economy enters a recession, for the Ocean gate who sells hard drives for $\$200$ each, fixed costs are $\$30$ millions and variable costs are $\$140$ millions, and corporate tax is $30\%$ .

Introduction:

Operating leverage means a relationship between fixed and variable costs. A business which has a higher contribution margin and lower variable cost have high operating leverage.

If the economy enters s recession, then, the prices of product get high and sales starts a decline.

Answer to Problem 27PS

The percentage decline in sales is $100\%$ at the time of recession.

Explanation of Solution

Given:

At the time of recession, it will sell only half of the sale volume.

Sales in a strong economy is $2\text{ millions}$

Sales in recession is $\text{1 million}$

Sale price per unit is $\$200$

If the economy enters a recession, then, the prices of product get high and sales starts declining.

Here,

In a recession,

  $\begin{array}{c}\text{Sales}=1\text{ million}\times \$200\\ =\$200\text{ millions}\end{array}$

In a strong economy,

  $\begin{array}{c}\text{Sales}=2\text{ millions}\times \$200\\ =\$400\text{ millions}\end{array}$

Hence,

  $\begin{array}{c}\text{\% change in sales}=\frac{\$400\text{ millions}-\$200\text{ millions}}{\$200\text{ millions}}\times 100\\ =100\%\end{array}$

So, percentage decline in sales is $100\%$ .

Summary Introduction

(b)

To determine:

The percentage decline in sales, if the economy enters a recession, for the Ocean gate who sells hard drives for $\$200$ each, fixed costs are $\$30$ millions and variable costs are $\$140$ millions, and corporate tax is $30\%$ .

Introduction:

Operating leverage means a relationship between fixed and variable costs. A business which has a higher contribution margin and lower variable cost have high operating leverage.

The economy drops down at the time of recession. So, the profit with high operating leverage firm will reduce drastically.

Answer to Problem 27PS

The percentage decline in profits is $200\%$ at the time of recession.

Explanation of Solution

Given:

At the time of recession, it will sell only half of the sale volume.

Sales in a strong economy is $2\text{ millions}$

Sales in recession is $\text{1 million}$

Sale price per unit is $\$200$

Variable cost per unit is $\$140$

Fixed Cost is $\$30\text{ millions}$

Corporate tax is $30\%$

If the economy enters recession prices of product gets high and profit will get reduced.

Here,

In a recession economy,

  $\begin{array}{c}\text{Sales}=1\text{ million}\times \$200\\ =\$200\text{ millions}\end{array}$

  $\begin{array}{c}\text{Total Cost}=\$30\text{ millions}+\left(\text{1 million}\times \$140\right)\\ =\$170\text{ millions}\end{array}$

  $\begin{array}{c}\text{Profit before tax}=\$200\text{ millions}–\$170\text{ millions}\\ =\$30\text{ millions}\end{array}$

In a strong economy,

  $\begin{array}{c}\text{Sales}=2\text{ millions}\times \$200\\ =\$400\text{ millions}\end{array}$

  $\begin{array}{c}\text{Total Cost}=\$30\text{ millions}+\left(2\text{ millions}\times \$140\right)\\ =\$310\text{ millions}\end{array}$

  $\begin{array}{c}\text{Profit before tax}=\$400\text{ millions}–\$310\text{ millions}\\ =\$90\text{ millions}\end{array}$

Now,

  $\begin{array}{c}\text{\% change in sales}=\frac{\$90\text{ millions}-\$30\text{ millions}}{\$30\text{ millions}}\times 100\\ =200\%\end{array}$

So, percentage decline in profit is $200\%$ .

Summary Introduction

(c)

To determine:

By comparing decline in sales and decline in profits, measure the operating leverage of the Ocean gate who sells hard drives for $\$200$ each, fixed costs are $\$30$ millions and variable costs are $\$140$ millions, and corporate tax is $30\%$ .

Introduction:

Operating leverage means a relationship between fixed and variable costs. A business which has a higher contribution margin and lower variable cost have high operating leverage.

Answer to Problem 27PS

The operating leverage of the firm is high as change in profit is higher than the change in sales.

Explanation of Solution

  $\begin{array}{c}\text{Operating Leverage}=\frac{\text{\% change in profit}}{\text{\% change in sales}}\times 100\\ =\frac{200\%}{100\%}\\ =2\end{array}$

So, operating leverage of firm is 2