Question

X Company's accountant has developed the following budgeted revenue and cost functions for 2020: R =...

X Company's accountant has developed the following budgeted revenue and cost functions for 2020:

  • R = $30.12X
  • C = $20.37X + $325,000

where R is revenue, C is total cost, and X is units sold.

Assuming a tax rate of 30%, how many units must X Company sell in 2020 in order to earn $276,000 after taxes?

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Answer #1

Net Profit Before Taxes = Net Profit After Taxes / (1 - Tax Rate)

Net Profit After Taxes = $ 276,000

Tax Rate = 30%

1- Tax Rate = 1 - 30% = 70%

Net Profit Before Taxes = ?

Net Profit Before Taxes = 276,000 * 100/70

Net Profit Before Taxes = $ 394,286

Calculation of Units to be sold to earn Net Profit Before Taxes of $ 394,826

Net Profit Before Taxes = R - C

Where

R stands for Revenue

C stands for Total Cost

X stands for Units Sold

R = 30.12X

C = 20.37 X + 325,000

Net Profit Before Taxes = 30.12 - (20.37X + 325,000)

394,286 = 30.12 X - 20.37 X - 325,000

394,286 + 325,000 = 9.75X

9.75 X = 719,286

X = 719,286 / 9.75

X = 73,773 Units

Units Required to be sold to earn Target Profit of $ 276,000 after Taxes = 73,773 Units

Answer being rounded off due to fraction.

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