Macy’s Inc. (NYSE: M) will close as many as 40 stores next year, which the company says represents only 1% of its revenue. The department store chain has 770 stores, so the math shows why the stores are “underperforming.” The decision is part of the new math of brick-and-mortar retail. Any troubled retailer has to have stores that do not make money. And at the top of that list are J.C. Penney Co. Inc. (NYSE: JCP) and Sears Holdings Corp. (NASDAQ: SHLD), which owns Sears and K-Mart.

Macy’s CEO Terry J. Lundgren wants to keep his job, but he has two challenges that will make that difficult. One is that Macy’s stock has fallen to nearly a 52-week low. At least he can claim his company’s shares have done better than J.C. Penney and Sears, which are off 9% and 14%, respectively. However, Lundgren has made $42 million in the past three years. Investors and the Macy’s board might ask themselves what they have gotten for all that money.

Macy’s lost $126 million on revenue of $6.1 billion in the quarter that ended August 1. Sears made $208 million in the same period on $6.2 billion in sales. However, Sears had a gain of $526 million in the sale of assets. According to the Sears Holdings 10-Q, the company has 1,702 Sears and K-Mart stores in the United States. J.C. Penney lost $138 million in the quarter that ended August 1, on revenue of $2.9 billion. It has 1,020 stores.

Sears and J.C. Penney have balance sheet problems that Macy’s does not have, which puts store-by-store performance under particularly heavy pressure. Once again, all retailers with a large number of stores must have some that underperform. That case is more certain when a retailer loses money.

J.C. Penney and Sears will close stores. The outstanding issue is how many, and what it will cost them in terms of charges that would include, among other things, severance, inventory liquidation and possibly lease termination. Even with these costs, the trimming is inevitable.

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The problems these department stores have, from the outside, will only get worse. The first among these is Amazon.com Inc. (NASDAQ: AMZN), which is appropriately called the greatest enemy of brick-and-mortar stores, and has been for years. Even if Wal-Mart Stores Inc. (NYSE: WMT) and Target Corp. (NYSE: TGT) also have suffered, their huge footprints and reasonable e-commerce efforts create another stifling challenge.

Cutting is a harsh way to survive, but for J.C. Penney and Sears, it is the only option.

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