ITPEC IP April 2020 Question 70
The operating profit when the sales quantity of a product is 700 units is as shown in the table below. When the unit sales price is reduced by 20% to expand sales, the sales quantity increases by 20%. How much, in yen, is the operating profit at this time? Here, the variable cost per one (1) unit of the product does not change.
Unit: Yen
Explanation
204,000 yen — rebuild sales and variable cost from per-unit figures at the new price and quantity; fixed cost stays the same.
- •Unit price: 700,000 ÷ 700 = 1,000 yen; unit variable cost: 140,000 ÷ 700 = 200 yen
- •New price: 1,000 × 0.8 = 800 yen; new quantity: 700 × 1.2 = 840 units
- •New sales: 800 × 840 = 672,000 yen; new variable cost: 200 × 840 = 168,000 yen
- •Operating profit: 672,000 − 168,000 − 300,000 = 204,000 yen
Answer (b)
Why not others:
- •(c) 260,000 — the current profit, as if a 20% price cut and a 20% volume rise cancelled out; in fact sales fall to 0.8 × 1.2 = 0.96 of the original while variable cost rises by 20%
- •(a) 200,000 and (d) 320,000 — neither matches price × quantity minus variable cost at 200 yen per unit minus the unchanged 300,000 fixed cost
Key rule: When price and volume change by the same percentage they do not cancel: revenue scales by the product of the factors, variable cost scales with volume only, and fixed cost does not change.
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