{
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  "question": "A business has $50000 in fixed costs, sells each unit for $25, and pays $15 in variable cost per unit. How many units must it sell to break even?",
  "answer": "5,000 units",
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    {
      "label": "Principles of Corporate Finance",
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    }
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  "source": {
    "kind": "edition_page",
    "value": "Brealey, Myers, Allen, Principles of Corporate Finance, 13th ed., Chapter 10, section on break-even analysis",
    "retrieved_utc": "2026-09-30T19:31:29Z"
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    "name": "Break-even units",
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  "method_deck": {
    "inputs": [
      {
        "name": "fixed_cost",
        "type": "number",
        "unit": "currency units",
        "required": true,
        "description": "Total fixed costs for the period",
        "min": 0
      },
      {
        "name": "unit_price",
        "type": "number",
        "unit": "currency units",
        "required": true,
        "description": "Selling price per unit",
        "min": 0
      },
      {
        "name": "unit_variable_cost",
        "type": "number",
        "unit": "currency units",
        "required": true,
        "description": "Variable cost per unit",
        "min": 0
      }
    ],
    "outputs": [
      {
        "name": "break_even_units",
        "unit": "units",
        "description": "Units needed to break even, rounded up to the next whole unit"
      },
      {
        "name": "contribution_margin",
        "unit": "currency units",
        "description": "Unit price minus unit variable cost"
      }
    ],
    "steps": [
      "contribution_margin = unit_price - unit_variable_cost; this must be greater than 0 or break-even is impossible.",
      "break_even_units (exact) = fixed_cost / contribution_margin.",
      "Round break_even_units up to the next whole unit (a business cannot sell a fraction of a unit).",
      "Round contribution_margin to 2 decimals (money to cents)."
    ],
    "constants": [],
    "examples": [
      {
        "name": "worked example",
        "inputs": {
          "fixed_cost": 50000,
          "unit_price": 25,
          "unit_variable_cost": 15
        },
        "expected": {
          "answer": "5,000 units"
        },
        "check": "hand computation: contribution_margin = 25-15 = 10.00; break_even = 50000/10 = 5000, already whole"
      },
      {
        "name": "test vector: non-integer result rounds up",
        "inputs": {
          "fixed_cost": 10000,
          "unit_price": 12,
          "unit_variable_cost": 9
        },
        "expected": {
          "answer": "3,334 units"
        },
        "check": "hand computation: contribution_margin = 12-9 = 3.00; break_even = 10000/3 = 3333.33..., rounds up to 3334"
      }
    ],
    "disclaimer": null,
    "deck_category": "finance"
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          "value": "Brealey, Myers, Allen, Principles of Corporate Finance, 13th ed., Chapter 10, section on break-even analysis",
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}