A new study shows the price Dallas or Austin could pay if Amazon picks either Texas city for its second headquarters. Data and analytics provider CoStar Group forecasts both cities will see a 10-year rise in apartment rents if either lands Amazon’s so-called HQ2 project — but Austin rents would increase more than those in Dallas.

Dallas-Fort Worth would see a modest increase in apartment rents if the Amazon project comes here, the study suggests. CoStar predicts DFW rents will go up 14.8 percent from 2018 to 2028 without HQ2 (from $1,116 to $1,281) and 17 percent with HQ2 (from $1,116 to $1,307). By itself, HQ2 would be responsible for a $26-a-month rise in DFW rents during that period.

By comparison, CoStar forecasts that without HQ2, the average apartment rent in the Austin area will jump from $1,206 a month this year to $1,450 in 2028, or 20.2 percent. But if HQ2 does settle there, rent would climb from $1,206 to $1,553 during the same period, or 28.8 percent, the CoStar report says. In other words, HQ2 alone could cause a $103-a-month surge in Austin rents from 2018 to 2028.

The estimates apply to apartments of all sizes.

Among the 16 U.S. metro areas that are finalists for HQ2, Raleigh, North Carolina, would experience the biggest spike in rental rates, the CoStar study says, followed by Nashville, Tennessee, Columbus, Ohio, and then Austin.

CoStar is the latest group to make predictions about the housing markets in cities Amazon is considering.

Apartment List, an online marketplace for apartment hunters, forecasts rents will climb an extra 0.2 percent to 0.4 percent in DFW if HQ2 ends up here. In Austin, it could be 0.8 percent to 1 percent a year.

Earlier this year, a report from Amherst Capital Management LLC, a real estate investment firm, predicted demand for single-family homes in the Dallas metro area would inch up by just 4 percent if this region scores HQ2. By comparison, the Austin metro area would jump by 13 percent.

And Mr. Cooper, a Dallas-based mortgage lender, forecasts home values in Austin will rise 5.9 percent from June 2018 to June 2019 without HQ2 and 15.8 percent with HQ2. For Dallas, those same numbers would be 3.7 percent and 12.4 percent.

For both Austin and Dallas, “home prices would see some uplift from a favorable Amazon announcement,” Mr. Cooper says, “but it won’t be profoundly different from the current trajectory.”