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An Asahi Shimbun column last May carried an Osaka reader’s tip on how to save small change at McDonald’s.

A 59 yen hamburger at the time came to 61 yen with the 5 percent consumption tax.

But the cost of two burgers purchased together came to 123 yen, based on a calculation that figures the tax in fractional terms. To buy two burgers separately, the price would only be 122 yen.

The extra 1 yen comes from rounding off the fractions.

The 59 yen hamburger, when 5 percent of its price is calculated and added on, comes to 61.95 yen, which is rounded off to the nearest 1 yen.

Since the yen does not have units smaller than one, stores round off the fractions to the lesser value. The calculation for two hamburgers would be 59 yen × 2 × 1.05 = 123.9 yen, or 123 yen at the cash register.

But under the new tax-inclusive price display law that takes effect Thursday, the fractional amounts must be posted under pricing conditions that warrant it, posing a potential headache for cost-conscious consumers, and stores.

The new law requires all price tags to show exactly what the total cost of a product will come to, including the consumption tax.

And even if rounded-down fractions re-emerge with multiple purchases, stores will not be allowed to charge more than the simple sum of the prices printed on tags.

Because it will be up to retailers to decide how to treat fractions, price differences are inevitable.

In the case of many major supermarkets, fractions will be rounded down.

A chocolate bar that cost 150 yen minus the tax will now carry a price tag of 157 yen, after rounding down from 157.5 yen.

Before Thursday, two would cost 315 yen (150 yen × 2 × 1.05 = 315 yen), but under the new tax-included price of 157 yen, you will only pay 314 yen for two because the stores will not be allowed to charge more than the sum of what the original price tag shows.

Ito-Yokado Co. and other supermarkets adopting this method said the resulting disparity will be to their loss, which they will try to absorb.

The situation is a little different at convenience stores. Many said they will round fractions of 0.5 yen and over upward, or downward for those under 0.5 yen, which is the common practice for rounding off fractions.

Thus the 150 yen chocolate bar (150 yen × 1.05 = 157.5 yen) with tax will be 158 yen.

Convenience store officials said ignoring all fractions would be financially too burdensome. Since purchases are usually small, it would be difficult to absorb potential losses through volume sales, they said.

What complicates the new law is that there will also be price differences between stores that have updated their cash register systems and those that have not.

Major supermarkets and convenience stores have updated their systems for tax-included prices, so prices on tags are simply added up.

Most department stores will continue using the old system, which adds up tax-excluded prices and multiplies the sum by 1.05 at each register. In this case, fractions will emerge.

To keep prices at the level posted before the law went into effect, most department stores plan to round up fractions on price tags but charge shoppers on a rounded-down basis at the register.

The 150 yen chocolate bar’s price tag would say 158 yen, but the cashier would only charge 157 yen (150 yen × 1.05 = 157.5 yen).

Two would be 150 yen × 2 × 1.05 = 315 yen, not 316 yen.

“You cannot charge more than the tax-included price, because that would be illegal. So we had no choice but to do it this way,” said Yukiteru Azukizawa, director of the Japan Department Stores Association.

But why not round down fractions and take the difference as a loss, like supermarkets are doing?

Azukizawa attributed the difference to the unique retail practice seen at department stores.

Most retail stores buy merchandise from suppliers and eat the loss if inventories go unsold.

But a large portion of department store merchandise is still owned by the suppliers, which set the prices and eat the loss from items unsold.

Since department stores don’t actually own the products, they are not in the position to round down fractions.

Were they to attempt this, they would risk violating fair competition laws that ban stores from using their dominant position to force suppliers to reduce prices, Azukizawa said.

While many retailers grapple with how to treat fractions, one supermarket chain has taken a different tack — posting fractions on price tags.

OK Corp., which has some 30 stores in the Tokyo area, displays the tax-included price without rounding fractions. A 150 yen chocolate bar carries a 157.50 yen price tag.

Shoppers who buy one would be charged 157 yen, but those who buy two would pay 315 yen, because the fractions would be carried to the final calculation.

“If we round up, customers have to pay more, but if we round down, we have to incur a loss,” said Junichiro Honda, spokesman for the chain. “This way neither side gets hurt.”

The chain, which has aggressively discounted prices, cannot endure further markdowns, he said.

“We are already offering the lowest price possible. We would go bankrupt if we cut it further.”

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