You sell a pizza for $20 and it costs you $15 to make it. If your fixed costs are $80,000 and you aim to make a
net income of $4’500 this month, how much must your dollar sales be? Assume your tax rate is 30%.

Question

BlackTom AI · Accepted Answer

Step-by-step analysis of the given problem and options (even though no options are provided, I will show the full reasoning):

- First, identify the relevant financial relationships. Each pizza sells for $20 and costs $15 to produce, so the contribution margin per pizza (sales minus variable cost) is 20 - 15 = $5 per pizza. This $5 contributes toward covering fixed costs and generating net income.

- Let n be the number of pizzas sold this month. Then the total contribution margin is 5n. The fixed costs are $80,000, so the pre-tax profit (income before tax) is: 5n − 80,000.

- The tax rate is 30%, so after-tax net income is 70% of the pre-tax profit: Net income = 0.70 × (5n − 80,000).

- The target net income is $4,500. Set up the equation and solve for n:
  0.70 × (5n − 80,000) = 4,500
  5n − 80,000 = 4,500 / 0.70 = 6,428.571...
  5n = 80,000 + 6,428.571... = 86,428.571...
  n = 86,428.571... / 5 = 17,285.714...

- Since you cannot sell a fraction of a pizza, round to the nearest whole pizza. The closest reasonable quantity is n ≈ 17,286 pizzas.

- Now convert this into total sales dollars. Each pizza sells for $20, so total sales (revenue) required is:
  Sales = 20 × 17,286 = 345,720.

- If you keep the exact fractional n for calculation, you get Sales ≈ 20 × 17,285.714... ≈ 345,714.29, which rounds to about $345,714 (or $345,720 depending on rounding convention). This aligns with the logic of covering fixed costs and achieving the after-tax profit target.

What went wrong with other possible intuitions: some might try to ignore taxes or fixed costs, or misapply the tax on revenue rather than on profit. Here, the tax applies to pre-tax profit, not to the revenue, and fixed costs must be recovered before any net income is realized, so the correct approach involves solving for n using the after-tax profit equation above and then converting to sales dollars.

Final takeaway: to achieve a post-tax net income of $4,500 given $80,000 fixed costs, a $5 per-unit contribution margin, and a 30% tax rate, you need to sell about 17,286 pizzas, resulting in approximately $345,714 in sales.

You sell a pizza for $20 and it costs you $15 to make it. If your fixed costs are $80,000 and you aim to make a net income of $4’500 this month, how much must your dollar sales be? Assume your tax rate is 30%.Numerical

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You sell a pizza for $20 and it costs you $15 to make it. If your fixed costs are $80,000 and you aim to make a net income of $4’500 this month, how much must your dollar sales be? Assume your tax rate is 30%.

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