Head-First Company plans to sell 5,800 bicycle helmets at $76 each in the coming year. Unit variable cost is $44 (includes direct materials, direct labor, variable factory overhead, and variable selling expense). Total fixed cost equals $49,600 (includes fixed factory overhead and fixed selling and administrative expense). Required: 1. Calculate the number of helmets Head-First must sell to earn operating income of $89,600. 2. Check your answer by preparing a contribution margin income statement based on the number of units calculated.

1.  4350 Units

2.  

                            Contribution margin income statement

                                                             Amount in $

Sales                                                       330,600

Variable expenses                                 (191,400)

Contribution margin                               139,200  

Fixed expenses                                       (49,600)          

Net operating income                            89,600  

Explanation:

The BEP which is the break even point is the point where the company's sales or revenue generated is equal to the cost incurred. As such, the BEP is the number of units that must be sold for the company to make neither a profit nor a loss.

Both sales and variable cost are dependent on the number of units sold.

The sales less the variable cost gives the contribution margin. The contribution margin less the fixed cost gives the net operating income.

Let the number of helmets to be sold to earn the net operating income be B

Then

76B - 44B - 49,600 = 89,600

32B = 89,600 + 49,600

32B = 139200

B =  139200 /32

= 4350 Units

Sales = $76 * 4350

= $330,600

Variable cost = $44 * 4350

= $191,400