If the company is in any way a decent place to work, they will have a clue and "So we don't have to spend 2x as much over the next year replacing them, with rec

If the company is in any way a decent place to work, they will have a clue and "So we don't have to spend 2x as much over the next year replacing them, with recruiters' fees, lost productivity, and the fact that someone to do all the work they were doing will demand more money" will work as a reason why. When someone leaves due to being underpaid, if they are at all good at their job (and especially if they were hired at a low rate and have grown in capability during their time there), their former employer will usually end up spending more than the old employee wanted in the first place with all the inherent costs of hiring a replacement.