ALWAYS use use strict; use warnings;!

use v5.14; has the side effect of doing use strict;, so that's good.

But use warnings; is missing. And using it would have caught some errors in your program.

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The arguments being passed to fib make no sense.

You should originally pass the first and second terms (0 and 1), but you don't do that.

On the second pass, you should pass the second and third terms, but you don't do that either.

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my $increment = @_; doesn't do what you think it does. An array in scalar context produces the number of elements in the array. You want

# `my ( ... ) = ...` evaluates the RHS in list context.
my ( $increment ) = @_;
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or

# `shift` is short for `shift( @_ )`
my $increment = shift;
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The program should output complete lines.

print $result;
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should be

print "$result\n";
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or

say $result;
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This is just a style thing, but

$result += $increment;
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is cleaner than

$result = $result + $increment;
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as Fletch pointed out.

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Another style thing: 4000000 can also be written as 4_000_000.