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# Units of Each Product to Achieve Required Income After-Tax

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Company. sells 4 different products in a mix of 9:5:4:2 respectively. The sales prices, respectively, are \$13, \$17, \$10 and \$12. Product A has variable costs of \$8 and product B of \$12. The contribution margin percentage for C is 40% and for D 25%. Fixed costs are \$460,000. In the coming year the company wants to make a profit of \$96,600 after tax. The tax rate is 30%.
Required: 1. Determine the units of each product which must be sold to achieve the required income after tax.
2. Prepare an income statement which proves that your answer in # 1 is correct.

Here is what I have determined thus far. Please advise if I am going in the right direction. This is graduate level work.

Products A B C D
Sales 13 17 10 12
V/C 8 12 ? ?
Mix 9 5 4 2
CM % ? ? 40 25

Contribution Margin for Product A = 13-8/13 = 38%
Contribution Margin for Product B = 17-12/17= 29%
Variable Cost for Product C = 10 - (.40 X 10) = 6
Variable Cost for Product D = 12 - (.25 X 12) = 9
Products A B C D
Sales 13 17 10 12
V/C 8 12 6 9
Mix 9 5 4 2
CM % 38 29 40 25

Break Even = FC/CM
FC = \$460,000
CM = ?
Total Contribution Margin = (9 X 38) + (5 X 29) + (4 X 40) + (2 X 25) = 697
Break Even = 460,000/697 = 659.97

The number of product A that must be sold to Break Even = 659.97 X 9 = 5,939.73 Dollars Equal \$77,216.49
The number of product B that must be sold to Break Even = 659.97 X 5 = 3,299.85 Dollars Equal \$56,097.45
The number of product C that must be sold to Break Even = 659.97 X 4 = 2,639.88 Dollars Equal \$26,398.80
The number of product D that must be sold to Break Even = 659.97 X 2 = 1,319.94 Dollars Equal \$15,839.28
Total Units of all products that must be sold to Break Even = 13,199.40 Dollars Equal \$175,552.02

Check Work:
Average CM = 697 / 20 = 34.85
FC/ Average CM = 460,000/ 34.85 = 13,199.43 (Total Units Needed to be sold)
A = 13,199.43 X 9 =

Profit after tax = 96,600 Tax Rate = 30% 96,600 / 1-.30 = 138,000
CHECK WORK = 138,000 X .30 = 41,400 - 138,000 = 96,600
New BE or Profit after Tax = FC + Profit / CM = 460,000 + 138,000 / 697 = 857.96

The number of product A that must be sold to Break Even or Make After Tax Profit =857.96 X 9 = 7,721.64
The number of product A that must be sold to Break Even or Make After Tax Profit =857.96 X 5 = 4,289.80
The number of product A that must be sold to Break Even or Make After Tax Profit =857.96 X 4 = 3,431.84
The number of product A that must be sold to Break Even or Make After Tax Profit =857.96 X 2 = 1,715.92
Total Units of all products that must be sold to Break Even or Make After Tax Profit = 17,159.20

Check Work:
Average CM = 697 / 20 = 34.85
FC/ Average CM = 460,000 + 138,000 / 34.85 = 17,159.25 (Total Units Needed to be sold)
A = 17,159.25 X 9 = 154,433.25

Income Statement
Product A Product B Product C Product D
Sales 77,216.49 56,097.45 26,398.80 15,839.28
Variable Cost 47,517.84 39,598.20 15,839.28 11,879.46
Contribution Margin 29,698.65 16,499.25 10,559.52 3,959.82
Fixed Expenses 46,0000 46,0000 46,0000 46,0000
Net Operating Income.