Neptune Company produces toys and other items for use in beach and resort areas. A small, inflatable toy has come onto the market that the company is anxious to produce and sell. The new toy will sell for $3.30 per unit. Enough capacity exists in the company’s plant to produce 30,200 units of the toy each month. Variable expenses to manufacture and sell one unit would be $2.08, and fixed expenses associated with the toy would total $54,766 per month. The company's Marketing Department predicts that demand for the new toy will exceed the 30,200 units that the company is able to produce. Additional manufacturing space can be rented from another company at a fixed expense of $2,738 per month. Variable expenses in the rented facility would total $2.31 per unit, due to somewhat less efficient operations than in the main plant. Required:
1. What is the monthly break-even point for the new toy in unit sales and dollar sales?
2. How many units must be sold each month to attain a target profit of $12,474 per month?
3. If the sales manager receives a bonus of 20 cents for each unit sold in excess of the break-even point, how many units must be sold each month to attain a target profit that equals a 29% return on the monthly investment in fixed expenses?

1) Break-even point in unit sales: 51,680 units

  Break-even point in dollar sales: $144,704

2) The units that must be sold each month to attain a target profit of $12,474 per month are:

= 63,669 units

3) The units that must be sold each month to attain a target profit that equals a 29% return on the monthly investment in fixed expenses are:

= 108,574 units

Explanation:

 1. On the first 30,200 units  

Sales price              $3.30

Variable expenses     $2.08

Contribution margin   $1.22

Above 30,200 units  

Sales price               $3.30

Variable expenses       $2.31

Contribution margin    $0.99

Fixed cost for initial 30,200 units= $54,766

Less: Contribution Margin (30,200 units * $1.22) + $36,844

Remaining uncovered cost = $17,922 ($54,766 - $36,844)

Monthly rental for additional space = $2,738

Total fixed costs covered by remaining sales = $20,660 ($17,922 + $2,738)

Required units = $20,660 / 0.99 = 20,869 units

Breakeven units = 30,200 + 20,869= 51,069 units

51,069 * $3.3 = $168,528

2)  

Working: $12,474 / 0.99 = 12,600 units

Thus total units = 51,069 + 12,600 = 63,669

3)  

Working: Desired monthly expenses: $54,766 + $2,738 = 57,504

57,504 * 20% = 11,501

Unit contribution margin: 0.99 - 0.20 = 0.79

Contribution margin = Target profit / Unit contribution margin = 11,501 / 0.20 = 57,505 units

51,069 units + 57,505 units = 108,574 units

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