The British company that owns Terminix pest control warned of softening demand in North America, and investors are worried things could get worse from here. Shares of Rentokil Initial (RTO 0.61%) fell as much as 20% on Thursday morning due to what the company called "challenging" macroeconomic conditions.

Higher rates are eating into growth

Rentokil is a global bug buster, operating in 90 countries offering not just pest control but also cleaning and sanitizing services as well. Last year, the company acquired Terminix Global Holdings for $6.7 billion, and North America now accounts for almost half of total sales.

It appears that the acquisition might not pay off as quickly as management had hoped. Rentokil reported overall North America revenue up 2.2% in the third quarter but said its U.S. products wholesale distribution business was down 2.5% due to lower demand for chemical products.

"While customer retention rates remained resilient, new residential customer acquisition was challenged by the macroeconomic backdrop and a softer consumer demand environment," Rentokil said in a statement.

The company now expects its full-year operating margin to come in at 18.5% and 19%, down from previous guidance of 19.5%.

Should you buy the dip on Rentokil?

To some extent the company saw the sluggishness coming. Late in the second quarter, Rentokil saw ominous trends in pest control digital search volumes and reduced lead flow. Inflation and higher interest rates are likely to cause some belt-tightening, and households forced to choose between making mortgage payments or pest control are likely to live with pests.

Higher rates have also eaten into housing sales, which means fewer new households in need of pest control services.

With Thursday's drop, Rentokil shares are now 30% below where they traded heading into 2022. Given the company's added bulk with Terminix in-house and the long-term need for pest control, there is ample opportunity for the stock to make back those losses and soar higher in the years to come.

But until the macro picture in the U.S. and elsewhere is more clear, it could be difficult for Rentokil shares to move significantly higher. Investors considering buying in here should know that significant patience will be required.