ITPEC IP October 2025 Question 72
The sales and the costs for a certain product for this month are as shown in the table below. When the unit sales price is changed from 1,000 yen to 800 yen, in order to avoid making a loss, at least how many units need to be sold each month? Here, the fixed cost and the variable cost per unit of the product do not change.
Explanation
6,000 units — at the new price each unit contributes only 100 yen towards the fixed cost of 600,000 yen.
- •Contribution margin per unit at the new price: 800 − 700 = 100 yen
- •Break-even quantity: 600,000 ÷ 100 = 6,000 units
- •Check: sales 6,000 × 800 = 4,800,000 yen, costs 600,000 + 6,000 × 700 = 4,800,000 yen, profit 0
At the old price the product was already exactly at break-even: 2,000 units × 300 yen margin = 600,000 yen. Cutting the price by 20% cuts the margin by two thirds, so the volume must triple.
Answer (d)
Why not others:
- •(a) 2,400 — raises the volume by the same 20% as the price cut, 2,000 × 1.2; it covers only 2,400 × 100 = 240,000 yen of the fixed cost
- •(b) 2,500 — keeps sales at 2,000,000 yen, 2,000,000 ÷ 800, ignoring that each unit still costs 700 yen; the loss is 350,000 yen
- •(c) 4,800 — the break-even sales amount, 600,000 ÷ (1 − 700 ÷ 800) = 4,800,000 yen, divided by the old price of 1,000 yen instead of the new 800 yen
Key rule: Break-even quantity is fixed cost ÷ (unit price − unit variable cost); a small price cut shrinks the margin by far more in relative terms, so the required volume rises sharply.
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