Is the code you pasted a simplified sample of the original? If not, I do not understand why you have the whole $stopvalue business in the first place. Your code progresses linearly, and the if ($stopvalue == 1) condition is pointless. At that point, $stopvalue is always set to 1.
Putting that point aside, unless you already know what fork and exec do, it would probably be best to avoid them. They are the low level primitives, and the other available methods are usually simpler and more convenient. Doing the fork/exec yourself should be reserved for times when you really need it.
In your case, I would lean toward a piping open, as it will provide enough control but also enough simplicity. As an added bonus, you'd be able to read the program's output, if necessary. Here's an example:
my $pid = open my $lsfh, "-|", "sleep", 10
or die "Cannot exec sleep: $!\n";
print "'sleep' is running in the background.\n";
print "The background process has a PID of $pid.\n";
waitpid $pid, 0;
print "All done.\n";