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Units of Each Product to Achieve Required Income After-Tax

Received the following Information:

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.

Solution Summary

The solution assists in determines the units of each product to achieve required income after-tax.

$2.19