module.exports = {
  slug: "break-even-units",
  title: "Break-even units",
  deck_category: "finance",
  description: "Computes the number of units a business must sell to cover fixed costs, given the unit price and unit variable cost.",
  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: [],
  sources: [
    { kind: "edition_page", value: "Brealey, Myers, Allen, Principles of Corporate Finance, 13th ed., Chapter 10, section on break-even analysis", title: "Principles of Corporate Finance", publisher: "McGraw-Hill", retrieved_utc: "2026-09-30T19:31:29Z", note: "Break-even units = Fixed costs / (Price - Variable cost per unit)" }
  ],
  disclaimer: null,
  questionText(inputs) {
    return `A business has $${inputs.fixed_cost} in fixed costs, sells each unit for $${inputs.unit_price}, and pays $${inputs.unit_variable_cost} in variable cost per unit. How many units must it sell to break even?`;
  },
  run(inputs) {
    const { fixed_cost, unit_price, unit_variable_cost } = inputs;
    if (typeof fixed_cost !== "number" || fixed_cost < 0) throw new Error("fixed_cost must be a non-negative number");
    if (typeof unit_price !== "number" || unit_price < 0) throw new Error("unit_price must be a non-negative number");
    if (typeof unit_variable_cost !== "number" || unit_variable_cost < 0) throw new Error("unit_variable_cost must be a non-negative number");
    const contribution_margin = Math.round((unit_price - unit_variable_cost) * 100) / 100;
    if (contribution_margin <= 0) throw new Error("unit_price must exceed unit_variable_cost for break-even to be possible");
    const break_even_units = Math.ceil(fixed_cost / contribution_margin);
    return {
      answer: `${break_even_units.toLocaleString("en-US")} units`,
      values: { break_even_units, contribution_margin }
    };
  },
  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"
    }
  ]
};