New construction and permits to build new homes fell to a five-month low in April. But homebuilder sentiment has rebounded in May, reaching its second-highest level since the recession.

Taylor Morrison Home Builders (TMHC), which operates in nine states, including California and Texas, had a robust quarter, with orders for homes growing by 33%.

Of course, demand, especially for starter homes, is outpacing supply for prospective homebuyers, with prices rising at the fastest pace in two and a half years.

CEO Sheryl Palmer says that inventory is tight across the US but there are still pockets of affordability that buyers should be scouting.

Where should first-timers be looking?

One-third of Taylor Morrison’s overall business is building homes for first-time buyers, and Palmer says Atlanta, Phoenix and parts of Florida have been making up the bulk of their business.

Despite a shortage in inventory, Palmer says she’s “feeling very good” about how bullish Americans are about buying homes.

“People are finally able to get back into the market after bad credit history and millennials that have been waiting and saving — they’re getting to that life stage. And, on the opposite end, the boomers [are looking to buy as well],” she told Yahoo Finance.

“Builders, coming from a business perspective, are sitting in a good spot right now,” says Svenja Gudell, chief economist at Zillow.

Gudell points out that builders like Taylor Morrison are thinking about their bottom line quite conservatively rather than overextending themselves.

“Homes are selling really quickly to a robust base of customers and homebuilders’ profit margins are quite good,” she says. “Builders tend to be more risk averse and aren’t trying to move too fast. They’re chugging along, focusing on high quality and low quantity. If I were a builder, I would feel good about the market too.”

Melody Hahm is a writer at Yahoo Finance, covering entrepreneurship, technology and real estate. Follow her on Twitter @melodyhahm.

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