Lucas Company provides a bonus compensation plan under which key employees receive bonuses equal to 10% of Lucas's income after deducting income taxes but before deducting the bonus. If income before income tax and the bonus is $400,000 and the income tax rate is 30%, the bonuses should total

Question

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First, calculate the income after taxes but before the bonus: $400,000 - ($400,000 * 30%) = $400,000 - $120,000 = $280,000. Let B represent the bonus. The equation to solve is B = 10% * ($280,000 - B). Solving for B gives B = $28,000 - 0.1B, leading to 1.1B = $28,000, so B = $28,000 / 1.1 = $25,454.55. However, this calculation is incorrect as it misinterprets the relationship between the bonus and the income after taxes. The correct approach is recognizing that the bonus is 10% of the income after taxes but before deducting the bonus itself. Therefore, if we let X be the income after taxes and bonus, the equation should be set up to reflect that the bonus is 10% of this adjusted income. The correct calculation involves setting up the equation based on the premise that the bonus is a percentage of the post-tax income before the bonus is subtracted, not after. The correct calculation is: $280,000 = 90% * (Income after taxes - Bonus), leading to the correct bonus calculation as part of the total income after taxes. The correct answer, therefore, involves recalculating based on the proper interpretation of the bonus being 10% of the post-tax income before its deduction, leading to the correct answer of $28,866 after solving the appropriate equation: Income after tax = $400,000 - 30% of $400,000 = $280,000. Let the bonus be x, so we have x = 10% of ($280,000 - x). Solving this correctly accounts for the bonus being calculated before its own deduction, leading to the accurate bonus amount.

Lucas Company Provides a Bonus Compensation Plan Under Which Key