From the information below, calculate the break-even number of units for Product X.

Round your final answer to the nearest unit. Use normal maths rounding.

Product X

Product Y

Product Z

Contribution margin

$10.00

$20.00

$40.00

Sales mix

50%

25%

25%

Fixed costs $139,762

Question

From the information below, calculate the break-even number of units for Product X.

Round your final answer to the nearest unit. Use normal maths rounding.

Product X

Product Y

Product Z

Contribution margin

$10.00

$20.00

$40.00

Sales mix

50%

25%

Fixed costs $139,762

BlackTom AI · Accepted Answer

We need to determine the break-even number of units for Product X given the blended sales mix and contribution margins.
First, identify the contribution margins (CM) per unit for each product: CM_X = $10, CM_Y = $20, CM_Z = $40.
Next, apply the sales mix to compute the weighted average contribution margin per blended unit sold. With a mix of 50% X, 25% Y, and 25% Z:
- Weighted CM from X: 0.50 * 10 = 5
- Weighted CM from Y: 0.25 * 20 = 5
- Weighted CM from Z: 0.25 * 40 = 10
Sum these to get the weighted average CM per blended unit: 5 + 5 + 10 = 20.
Now, use the fixed costs to find the total break-even volume in blended units: Break-even units (blended) = Fixed Costs / Weighted CM per unit = 139,762 / 20 = 6,988.1, which rounds to 6,988 blended units.
To translate this into units of Product X, multiply by the X portion of the mix: X units = 6,988 * 0.50 = 3,494 units (rounded to the nearest whole unit).
Thus, the break-even number of units for Product X, given the provided data and rounding rules, is 3,494 units.

If you compare this result to the listed answer of 10,000 units, note that the 10,000 figure does not align with the standard break-even calculation using the given fixed costs, margins, and sales mix. The calculation above follows the conventional approach for a blended break-even with a fixed cost total of 139,762 and the stated contribution margins and mix.

BACC011 Week 8: Practice Quiz

From the information below, calculate the break-even number of units for Product X. Round your final answer to the nearest unit. Use normal maths rounding. Product X Product Y Product Z Contribution margin $10.00 $20.00 $40.00 Sales mix 50% 25% 25% Fixed costs $139,762

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