Question

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 $3.40 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 $2.14, and fixed expenses associated with the toy would total $56,578 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 $2,829 per month. Variable expenses in the rented facility would total $2.38 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 $12,546 per month?

3. If the sales manager receives a bonus of 15 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 28% return on the monthly investment in fixed expenses?

(For all requirements, Round "per unit" to 2 decimal places, intermediate and final answers to the nearest whole number.)

Answer 1

Selling Price			$3.40	per unit
Capacity of the Plant			30200	unit
Variable Expense			$2.14	per unit
Fixed Expense			$        56,578
Demand Exceeded the capacity
Additional Space Fixed Cost			$2,829	per month
Variable Expense in rented facility			$2.38	per unit
Contribution Margin from main plant			$1.26	[$3.40-$2.14]
Contribution Margin from rented plant			$1.02	[$3.40-$2.38]
Breakeven sales is where contribution margin covers the fixed cost
Let x be the breakeven sales units and it is higher that 30,200 units then
Contribution Margin			= 30200*$1.26+ (X-30200 units)*$1.02
Total Fixed Cost			= $56578+$2829
			$ 59,407.00
Equating contribution margin with Total Fixed Cost X can be found
	$30200*$1.26 + (X-30200 units)*$1.02 = $59407
	$38052 + (X-30200 units)*$1.02 = $59407
	(X-30200 units)*$1.02 = $59407-$38052
	(X-30200 units) = $21355/$1.02
	X-30200 units = 20936.27
	X = 30200 +20936.27
	X = 51136.27
Monthly Breakeven (in units) = 51136.27 units = 51137 (approx)
Monthly Breakeven (in $) = 511367 units *Selling price p.u = 51137 uits*$3.40 = $173865.80
To make monthly profit of $12546, contribution margin should be equal to sum of fixed cost and expected profit
Contribution Margin			= 30200*$1.26+ (X-30200 units)*$1.02
Total Fixed Cost + Profit			= $56578+$2829 + $12546
			$ 71,953.00
Equating contribution margin with Total Fixed Cost + Target Profit, 'X' can be found
	$30200*$1.26 + (X-30200 units)*$1.02 = $71953
	$38052 + (X-30200 units)*$1.02 = $71953
	(X-30200 units)*$1.02 = $71953-$38052
	(X-30200 units) = $33901/$1.02
	X-30200 units = 33236.27
	X = 30200 +33236.27
	X = 63436.27
Monthly units required (X) = 63436.27 units = 63437 (approx)
Monthly units (in $) = 63437 units *Selling price p.u = 63437 uits*$3.40 = $216026
Return Required = 28% of fixed investment
Profit Required = 28% of Fixed Cost = 28% ($56578+$2829) = $16634
Bonus paid to Sales Manager = $0.15 per unit excess of breakeven
Break even units = 51137 units
Total Contribution		= 30200*$1.26+ (X-30200 units)*$1.02 + (X-51137)*0.15
Total Fixed Cost + Profit			= $56578+$2829 + $16634
			$ 76,041.00
Equating contribution margin with Total Fixed Cost + Target Profit, 'X' can be found
	30200*$1.26+ (X-30200 units)*$1.02 + (X-51137)*0.15 = $76041
	$38052 + (X-30200 units)*$1.02 + (X-51137)*0.15= $76041
	(X-30200 units)*$1.02 + (X-51137)*0.15= $76041-$38052
	1.02X - 30804 + 0.15X - 7670.55 = $37989
	1.17X-38474.55 = $37989
	1.17X = $37989 +38474.55
	X = $76463.55/1.17
	X = 65353.46
Monthly units required (X) = 65353.461 units = 65354 (approx)
Monthly units (in $) = 65354 units *Selling price p.u = 65354 units*$3.40 = $2,22,204