How to make a new “Beverly Hills Cop” movie? It’s a question that has long vexed Hollywood. Brett Ratner tried for years to crack the case, though, judging from a 2010 Empire magazine interview, it’s fair to wonder how much progress he ever made. “Like, where do we start?” he wondered.

Like, where, indeed? Among the obstacles puzzling those who attempted to revive the franchise: Is Axel retired? Is he in Beverly Hills? Is he on vacation? Does Judge Reinhold reprise his role as Billy Rosewood?

In hindsight, this all seems unnecessarily complicated. From the moment the Don Simpson/Jerry Bruckheimer Films lightning bolt logo comes on the screen in Netflix’s “Beverly Hills Cop: Axel F” (streaming July 3), followed by the wailing sax riff of “The Heat Is On,” you realize that everyone involved understood the assignment. The solution to creating a new “Beverly Hills Cop” movie was to simply make the first one all over again.

“Beverly Hills Cop” came out 40 years ago, an anniversary that will alarm the segment of moviegoers who remember seeing it in theaters, and perhaps astound some just now realizing that Murphy was only 23 when he made it. The movie topped the box office 13 weeks running, selling 67 million tickets and, adjusted for inflation, still stands as the highest-grossing R-rated film of all-time. Coming on the heels of his work on “Saturday Night Live,” “48 Hrs.” and “Trading Places,” it certified Murphy as a movie star.

You had to be there. And if you weren’t (but especially if you were), “Beverly Hills Cop: Axel F” has been designed to function as a carefully calibrated time machine to take you back to the days when synth pop ruled the airwaves, you could disable a car by putting a banana in its tailpipe and a suite at a swanky Beverly Hills hotel went for $235 a night. (The price, we learn in “Axel F,” has gone up considerably.)

The formula for making a “Beverly Hills Cop” movie goes like this: You start in Detroit, Axel’s hometown, and spend a good chunk of time and money on a chase involving cars and trucks and, in the case of “Axel F,” a snow plow. Axel is operating outside the police rule book, and when this opening scene is over, after a great deal of mayhem and destruction, his shouting boss lets him know that this time, he has really gone too far. And he’d better not do anything like that ever again! (This time it’s Paul Reiser reading him the riot act.)

But the reprimand doesn’t really register because Axel was right. He’s always right. In fact, he’s never more right than when everyone tells him he’s wrong. That’s part of the character’s appeal.

Then something happens that necessitates a trip to L.A., specifically the 90210. In “Axel F,” it’s a call from Billy Rosewood (Judge Reinhold), still lovable and now in danger because he’s close to learning the truth about a police cover-up. And Billy’s not the only one in peril. Axel’s estranged daughter, Jane (Taylour Paige), is entangled in this mess too, thanks to her job as a criminal defense attorney.

Stakes established, Axel heads to Beverly Hills, where he shrewdly talks his way out of trouble, shares a scene with Bronson Pinchot’s excessively accented Serge, teaches the local authorities a thing or two about police work and, on occasion, demonstrates a sly understanding of racial relations in America. (Told not to reach for his ID by a police officer in “Axel F,” Axel replies, “I’ve been a cop for 30 years. I’ve been Black a whole lot longer. Trust me. I know better.”)

Then there’s a final showdown, showcasing the need to remove your sunglasses while operating a submachine gun, a little more bopping around to Harold Faltermeyer’s synth-pop ditty “Axel F,” the equivalent of a group hug between Murphy, Reinhold and John Ashton (returning as Det. Taggart, Billy’s partner and cranky BFF) and roll credits.

You might not remember this, but the first “Beverly Hills Cop” movie earned an Oscar nomination for original screenplay. Were voters aware that Murphy improvised most of his dialogue to the point that his co-stars could not keep from breaking? Maybe this was a hat tip. Murphy was that good.

You also might not know that there was a third “Beverly Hills Cop” movie, the 1994 entry Murphy has called “garbage.” One of the best lines in “Axel F” comes when Joseph Gordon-Levitt, a newcomer to the franchise playing a Beverly Hills police detective, leafs through Axel’s file and says, “And then, ’94. Not your finest hour.” The first two movies, along with “Axel F,” are streaming on Netflix. The third is not.

Promoting “Axel F,” director Mark Molloy is advertising the fact that he gave Murphy free rein to improvise. (Three writers — Will Beall, Tom Gormican and Kevin Etten — share screenplay credit. Props to whoever came up with the “not your finest hour” line.) Murphy is effective, even if the tone has shifted from a brash swagger to nostalgic cheer. The heat is gone.

But you knew that. Murphy is content to act his age, and the movie spends some time focusing on Axel’s attempts to reconnect with his daughter, a woman as headstrong as her father. And it’s hard to validate feelings when they’re drowned out by machine gun fire.

While it’s easy to view “Axel F” as a calculated cash grab, it’s clear that Murphy possesses an affection for the title character. From the get-go, Murphy’s portrayal hinged on Axel’s ability to warmly connect with everyone he meets. Even the villains like him. As Axel drives his blue Chevy Nova through the streets of Detroit during the new film’s opening credits, the city’s residents smile and wave (and sometimes flip him off) when he cruises by. They’re happy to see him. And so are we.