Chapter 7, Problem 55C

Niagra Falls Sporting Goods Company, a wholesale supply company, engages independent sales agents to market the company’s products throughout New York and Ontario. These agents currently receive a commission of 20 percent of sales, but they are demanding an increase to 25 percent of sales made during the year ending December 31, 20x2. The controller already prepared the 20x2 budget before learning of the agents’ demand for an increase in commissions. The budgeted 20x2 income statement is shown below. Assume that cost of goods sold is 100 percent variable cost.

The company’s sales manager, Joey Dulwich, is considering the possibility of employing full-time sales personnel. Three individuals would be required, at an estimated annual salary of $30,000 each, plus commissions of 5 percent of sales. In addition, a sales manager would be employed at a fixed annual salary of $160,000. All other fixed costs, as well as the variable cost percentages, would remain the same as the estimates in the 20x2 budgeted income statement.

Required:

1. 1. Compute Niagra Falls Sporting Goods’ estimated break-even point in sales dollars for the year ending December 31, 20x2, based on the budgeted income statement prepared by the controller.
2. 2. Compute the estimated break-even point in sales dollars for the year ending December 31, 20x2, if the company employs its own sales personnel.
3. 3. Compute the estimated volume in sales dollars that would be required for the year ending December 31, 20x2, to yield the same net income as projected in the budgeted income statement, if management continues to use the independent sales agents and agrees to their demand for a 25 percent sales commission.
4. 4. Compute the estimated volume in sales dollars that would generate an identical net income for the year ending December 31, 20x2, regardless of whether Niagra Falls Sporting Goods Company employs its own sales personnel or continues to use the independent sales agents and pays them a 25 percent commission.

To determine

Calculate the break-even point (in dollars) for N F S G Company.

Explanation of Solution

Break-Even Point: It is the point of sales at which entity neither earns a profit nor suffers a loss. It can also be said that the point of sales at which sales value of the entity recovers the entire cost of fixed and variable nature is called break-even point.

The formula to calculate the break-even point in sales dollars is as follows:

$\text{Break-even}\text{point}\text{in}\text{dollars}=\frac{\text{Fixed}\text{Costs}}{\text{Contribution}\text{Margin}\text{Ratio}}$

Contribution Margin ratio: It is a ratio that measures the contribution margin generated by the company from the sales to make it avialable for paying the fixed cost and generate a profit. It is expressed as percentage of margin available from each dollar sales to pay fixed expenses and to provide profit. The formula to calculate the contribution margin ratio is as follows:

$\text{Contribution}\text{Margin}\text{Ratio}=\frac{\text{Contribution}\text{Margin}}{\text{Sales}}\times 100$

Calculate the break-even point.

$\begin{array}{c}\text{Break-even point}=\frac{\text{Fixed expenses}}{\text{Contribution margin ratio}\left(\text{Working note}\left(\text{a}\right)\right)}\\ =\frac{\$100,000}{.2}\\ =\$500,000\end{array}$

Working note:

1. a) Calculate the contribution margin ratio.

$\begin{array}{c}\text{Contribution margin ratio}=\frac{\left(\begin{array}{l}\text{Sales}-\text{Cost of goods sold}\\ -\text{Variable expenses}\end{array}\right)}{\text{Sales}}\\ =\frac{\$10,000,000-\$6,000,000-\$2,000,000}{\$10,000,000}\\ =\frac{\$2,000,000}{\$10,000,000}\\ \end{array}$

$\begin{array}{c}\text{Contribution margin ratio}=\frac{\$8}{\$20}\\ =0.2\end{array}$

To determine

Calculate the estimated break-even point (in dollars) if the sales personnel are employed.

Explanation of Solution

Calculate the estimated break-even point (in dollars).

$\begin{array}{c}\text{Break-even point}=\frac{\text{Fixed expenses }\left(\text{refer table}\left(1\right)\right)}{\text{Contribution margin ratio}\left(\text{Working note}\left(\text{e}\right)\right)}\\ =\frac{\$350,000}{.35}\\ =\$1,000,000\end{array}$

Working notes:

1. b) Calculate the new fixed expenses.

New fixed expenses
Particulars	Amount ($)
Previous fixed expenses	$100,000
Sales personnel salaries (c)	90,000
Sales manager’s salary	160,000
Total	$350,000

Table (1)

1. c) Calculate the sales personnel salaries.

$\begin{array}{c}\text{Sales personnel salaries}=\text{Number of employees}\times \text{Annual salary for each}\\ =3\times \$30,000\\ =\$90,000\end{array}$

1. d) Calculate the new contribution margin.

Particulars	Amount ($)
Sales	$10,000,000
Cost of goods sold	6,000,000
Gross margin	$4,000,000
Commissions (at 5%)	500,000
Contribution margin	$3,500,000

Table (2)

1. e) Calculate the contribution margin ratio.

$\begin{array}{c}\text{Contribution margin ratio}=\frac{\text{Contribution margin}\left(\text{refer table}\left(2\right)\right)}{\text{Sales}}\\ =\frac{\$3,500,000}{\$10,000,000}\\ =.35\end{array}$

To determine

Calculate the sales volume (in dollars) to attain after- tax net income of $1,330,000.

Explanation of Solution

Target Profit: It refers to the desired amount of profit that a company expects to achieve by the end of an accounting period after it reaches its break-even point. Thus, the company needs to compute the required sales to earn the target profit.

Calculate the sales volume (in dollars).

$\begin{array}{c}\begin{array}{l}\text{Sales volume in dollars required}\\ \text{to earn target after-tax net-income}\end{array})=\frac{\text{Fixed expenses+}\frac{\text{Target after-tax net income}}{\left(1-\text{Tax}\text{rate}\right)}}{\text{Contribution margin ratio}}\\ =\frac{\$100,000+\frac{\$1,330,000}{\left(1-.30\right)}}{.15}\\ =\frac{\$100,000+\frac{\$1,330,000}{0.70}}{.15}\\ =\frac{\$100,000+\$1,900,000}{.15}\end{array}$

$\begin{array}{c}\begin{array}{l}\text{Sales volume in dollars required}\\ \text{to earn target after-tax net-income}\end{array})=\frac{\$2,000,000}{.15}\\ =\$13,333,333\left(\text{rounded}\right)\end{array}$

Calculate the new contribution margin ratio.

$\begin{array}{c}\text{Contribution margin ratio}=\frac{\text{Contribution margin}\left(\text{refer table}\left(3\right)\right)}{\text{Sales}}\\ =\frac{\$1,500,000}{\$10,000,000}\\ =0.15\end{array}$

Working note:

1. f) Calculation of new contribution margin by assuming sales commission increases to 25%.

Particulars	Amount ($)
Sales	$10,000,000
Cost of goods sold	6,000,000
Gross margin	$4,000,000
Commissions (at25%)	2,500,000
Contribution margin	$1,500,000

Table (3)

To determine

Calculate the sales volume (in dollars) to attain before- tax income is same under the two alternatives.

Explanation of Solution

There is no change in tax rate if the management chooses any one of the approach. We can find the sales volume so that the company’s before tax income is the same under the alternatives.

$\begin{array}{c}\left(\begin{array}{l}\text{Contribution margin ratio}\\ \times \text{Sales volume}\\ -\text{New fixed expenses}\end{array}\right)=\left(\begin{array}{l}\text{Contribution margin ratio}\\ \times \text{Sales volume}\\ -\text{Old fixed expenses}\end{array}\right)\\ \left(.35\times \text{Sales volume}-\$350,000\right)=\left(.15\times \text{Sales volume}-\$100,000\right)\\ .35\times \text{Sales volume}-.15\times \text{Sales volume}=\$350,000-\$100,000\\ .20\times \text{Sales volume}=\$250,000\\ \text{Sales volume}=\frac{\$250,000}{.20}\\ =\$1,250,000\end{array}$

If the sales volume is $1,250,000 the company will have the same before tax income under the two alternatives.